GRAPHIC METHODS
FOR
PRESENTING FACTS
WIZARD C. BRINTON
INDUSTRIAL MANAGEMENT LIBRARY
GRAPHIC METHODS
FOR
PRESENTING FACTS
BY
WILLARD C. BRINTOM
NEW YORK
THE ENGINEERING MAGAZINE COMPANY
1919
COPTBIGHT, 1914
BY THE ENGINEERING MAGAZINE COMPAICY
TO MY MOTHER
PREFACE
IN the preparation of this book there has been a constant effort to present the
subject to suit the point of view of the business man, the social worker, and the
legislator. Mathematics have been entirely eliminated. Technical terms are used
practically not at all. Since the readers whom it is most desired to reach are those
who have never had any statistical training, consistent effort has been made to keep
the whole book on such a plane that it may be found readable and useful by anyone
dealing with the complex facts of business or government. Though written primarily
for the non-technical man, it is hoped that this book may, nevertheless, prove con-
venient to the engineer, the biologist, and the statistician.
A definite effort has been made to produce a work which can serve as a hand book
for anyone who may have occasional charts to prepare for reports, for magazine
illustration, or for advertising. Unfortunately, there are extremely few draftsmen
who know how to plot a curve or prepare any kind of a chart from data presented to
them in the form of tabulated figures. Most draftsmen can plot a curve if they are
given the data and an example showing the general type of chart desired. The execu-
tive who desires a chart is usually too busy to stand by a draftsman and explain
in detail just how the chart should be prepared as concerns those all important
details of proportion, scale, width of line, etc. It is believed that the owner of this
book will find it feasible to run through the various chapters and pages until he finds
a chart most nearly like that which he desires to have made from his own data.
A sample chart placed before any draftsman of average ability should give the drafts-
man practically all the instruction needed for the preparation of a similar chart from
other data.
Much careful labor has been expended in so arranging the book that a busy
reader may get the gist of the matter by looking at the illustrations and reading only
the titles and the sub-titles. The main title under each illustration is intended to
show exactly what the chart represents, just as if it were used in some publication re-
lating to the particular subject matter of the chart. The sub-titles relate to method
and give criticism of each chart as a whole. Though the text gives much more de-
tailed information concerning method than can possibly be put into any sub-titles, the
reader who examines only the illustrations and the titles, without any reference to
the text, will undoubtedly get a major portion of the vital material in the book. It is
believed that an average reader may go through the illustrations and the titles in
about one hour.
Vi GRAPHIC METHODS
Many of the illustrations which have been borrowed for use in this book are
criticized adversely. It is the hope that all such criticisms will be accepted as an
honest attempt toward an advance in the art of showing data in graphic form. In
fairness to the authors of those charts which are criticized, it must be said that there
has been a very rapid advance in the art of graphic presentation within the last few
years and that many of these men would not present the material to-day by the
methods which may have been used some years ago in the preparation of certain
charts shown here. Where charts are used and criticized adversely, the charts have
been included only because it is felt that they show a practice which is rather common
but is nevertheless of questionable desirability.
Many of the suggestions for standard practice contained in this book should be
taken as tentative only. The American Society of Mechanical Engineers has invited
about fifteen of the chief American societies of national scope to co-operate by sending
one member each to a Joint Committee on Standards for Graphic Presentation.
Though this committee is not yet completely organized, and it will be some time before
any report is available, the reader who desires further information regarding standard
practice should be on the lookout for any reports which the joint committee may
publish in the future.
This volume may arouse in the minds of many readers a desire for more detailed
information than can possibly be given here. The following books are suggested
for the person who wishes to take up the study of statistics as related to the collection
and interpretation of data without special reference to the methods of graphic pres-
entation. The present work is necessarily limited to the consideration of graphic
presentation, and those who wish to go further in the general subject of statistics
should by all means consult books of the type exemplified by "The Elements of
Statistical Method," by Willford I. King, The Macmillan Company, New York;
"An Introduction to the Theory of Statistics," by G. Udny Yule, Griffin and Com-
pany, London; "Elements of Statistics," by Arthur L. Bowley, Charles Scribner's
Sons, New York; "Primer of Statistics," by W. Palin Elderton and Ethel M. Elderton,
Adam and Charles Black, London; "Statistical Averages," by Franz Zizek, Henry
Holt and Company, New York; "Statistical Methods with Special Reference to
Biological Variation," by C. B. Davenport, John Wiley and Sons, New York. Any
list of this sort is, of course, incomplete and these books are mentioned as only a few
of those which may be found useful to supplement the study of the subject considered
in this volume.
Part of the matter here presented was given in lectures delivered at the Graduate
School of Business Administration of Harvard University, the Amos Tuck School
of Administration and Finance of Dartmouth College, the Northwestern University
School of Commerce, and the College of Commerce and Administration of the Uni-
versity of Chicago. Some of the material was presented before the American Society
of Mechanical Engineers in New York. The advance presentation of matter in
course of preparation for the press was made with the cordial assent and approval of
the publishers of this work.
I am greatly indebted to Mr. Edward Scott Swazey, Mr. Curtis Prout, and Miss
Katherine Tyng, for valuable assistance and suggestions received during the prep-
aration of this book. Chapter XV is largely based on an article prepared at the
PREFACE Vll
suggestion of the author by Mr. Pierpont V. Davis of New York City and published
by Mr. Davis in Moody's Magazine. I wish also to express my thanks to numerous
friends who have given excellent suggestions and criticisms during the time the
manuscript was in preparation.
If this book should receive any commendation, much of that commendation will
be the result of good fortune in securing an unusually high grade of drafting skill on
those charts which are original.
The author cannot be responsible for the accuracy of the data presented in many of
the charts shown. The illustrations have been selected partly on account of the
educational value of the facts, but chiefly because of the methods used in presentation.
Though great care has been exercised to make the titles complete, the elaboration
of titles beyond their wording in the original source may have resulted in some in-
accuracies.
As far as the author is aware, there is no book published in any language covering
the field which it has been attempted to cover here. If the presentation of the
subject appears to be crude and incomplete, it is hoped that any critic will keep in
mind that there is little precedent for guidance in a territory so unexplored.
It is impossible entirely to avoid errors in any book containing as much detail as
results here from the numerous complex illustrations and the necessity of carefully
worded language to give condensed information. Any corrections, criticisms or
suggestions will be appreciated by the author.
WILLABD C. BEINTON
New York, June, 1914
CONTENTS
PAGE
CHAPTER I. COMPONENT PARTS . 1
The need for graphic methods in presenting facts. The method of pres-
entation as important as the data. Possibility for standard methods of
presentation. Tabulated figures versus graphic methods. A total shown
with its component parts. The horizontal bar. The circle and sectors.
Subdivision of components. Separate bars totalling 100 per cent. Charts
giving numerous subdivisions. Organization charts. Routing charts
for manufacturing plants and offices.
CHAPTER II. SIMPLE COMPARISONS .20
Errors due to comparing by areas or by volumes instead of by one
dimension only. The use of graphic methods in geography books. The data
should be shown on the face of each chart if possible. Good and bad
methods of including the data. "Eye-catchers" to attract the attention
of the reader. Criticisms of methods commonly used. Certain bars
made especially prominent. Increases and decreases. Lines connecting
different bars. Examples of various good methods.
CHAPTER III. SIMPLE COMPARISONS INVOLVING TIME 36
Impossibility of accurate interpretation when circles of different size are
compared. Errors when pictures of the human figure in different size are
compared. Methods which are popular and accurate as well. Examples of
bad practice in arrangement and the same data correctly represented.
Vertical bars giving the general effect of a simple curve. Curve plotting.
CHAPTER IV. TIME CHARTS 53
Horizontal bars drawn to a scale of time. Complex time charts by which
the relations of numerous horizontal bars may be studied. Time charts
showing bars combined with a curve expressing totals. Curves to study
whether time schedules are maintained. Rank charts to portray the rank of
different individuals at various times. Rank charts showing actual rela-
tive rank at any time and also changes in rank at various times. Tram-
dispatching charts. Time-distance curves.
ix
GRAPHIC METHODS
CHAPTER V. CURVE PLOTTING 69
The desirability of using only well-known methods of presentation.
Curves permit a more rapid and more accurate interpretation than possible
by other methods. Studies of the causes of crests and valleys of curves.
Curves especially needed for complex data. The use of curves in advertising.
Polar co-ordinates objectionable for presenting statistical data. Examples
of good practice in curve plotting.
CHAPTER VI. CURVE PLOTTING CONTINUED 84
Independent and dependent variables. Confusion caused if the inde-
pendent variable is not used for the horizontal scale. Examples showing
correct arrangement of scales. Curves to advertise newspaper circulation.
Curve charts combining much complex information. The use of two sets of
co-ordinate ruling for the vertical scale. Moving averages. Smoothing
curves. Index numbers. Weighted averages. Curve studies of national
prosperity.
CHAPTER VII. COMPARISON OF CURVES 107
Similarity and contrast of curves plotted in the same field. The zero
of the vertical scale should be shown on the chart. Advantages of plotting
curves for different years one above the other for comparison. Contrast
in shape of curves plotted in separate fields. Advantage from shading the
space under a curve. Numerous dissimilar but related curves on the same
sheet. Errors resulting if curves not having the same zero line are compared.
A total curve plotted from several other curves. Inverse relations, one curve
trending downward when another trends upward. Study of correlation
by plotting a curve from the data of two other curves. The angle of a curve
on ordinary rectangular co-ordinates tells nothing about the percentage rate
of growth. Disadvantages of the arithmetical scale ruling for curve
plotting. Advantages obtained by plotting curves on logarithmically ruled
paper.
CHAPTER VIII. COMPONENT PARTS SHOWN BY CURVES 138
Use of vertical bars with components totalling 100 per cent. Shaded
area under a curve when the height of the total field represents 100 per
cent. The use of several areas in a curve field which totals 100 per cent,
in height. A contrasting method of showing all curves plotted separately
but from the same zero line. Universal co-ordinate paper for convenience
in curve plotting. Total curves with component areas so that any point on
a curve totals 100 per cent for the height of the areas beneath.
CHAPTER IX. CUMULATIVE OR MASS CURVES 149
Factory production schedules and actual outputs plotted on a cumulative
basis. Curves for income and expense on a cumulative basis. Various uses
for cumulative curves. Cumulative curves with lines drawn to show rate
CONTENTS XI
PAGE
of change. A grand total cumulative curve plotted from several other
cumulative curves. Cumulative curves for the determination of storage
requirements for water supplies.
CHAPTER X. FREQUENCY CURVES. CORRELATION 164
The arrangement of objects so that their position shows a crude frequency
curve. Vertical bars to represent frequency. Frequency curves. The
"mode." Frequency curves much easier to interpret than charts using
bars or areas. Cumulative frequency curves. The use of cumulative
frequency curves for business problems. Cumulative frequency curves
preferably plotted on a "more than" basis instead of on a "less than"
basis. Necessity for making the independent variable the horizontal
scale. Wage comparisons for industrial work. Studies of the percentage of
clerical work and percentage of revenue from orders of various sizes. Pin
boards to record costs of doing work on orders of different size. Theoretical
curves for percentage of clerical work and percentage of revenue from
orders of different size. The Lorenz curve. Correlation curves. "Shot-
gun" diagrams. Plotting curves to represent numerous points. Shaded
areas to represent numerous dots. Correlation charts for two independent
variables. Isometrically ruled paper for chart work.
CHAPTER XI. MAP PRESENTATIONS , . . 208
Map presentation of prime importance. Shading of different areas. The
Ben Day method of mechanical shading. Lines of equality. Profiles.
Maps with circles or dots representing quantities. Shaded areas with a
key to represent quantity. Miscellaneous methods. Map charts showing
traffic. Map models with built up strips to show quantities.
CHAPTER XII. MAPS AND PINS 227
Map tacks projecting above the map. Map pins pushed in till the heads
touch the map. Photographing pin maps. Mounting maps for use with
map pins. Wall maps for use with pins. Map cabinet systems. Pin maps
for advertising work. Pins bearing identifying numbers. Spot maps to a
scale with each dot representing some large quantity. Routing systems.
Various types of pins and beads available. Bead maps and their great
advantages.
CHAPTER XIII. CURVES FOR THE EXECUTIVE 254
Peak-top curves versus flat tops. Methods for combining curves with
figures recording the data. Cards for plotting curves for operating records.
Advantages of the card method for instantaneous comparison of different
curves. Typical operating curves for a manufacturing business. Typical
records for a selling organization. Arrangement of the card system for exten-
sion with increase of business. Moving average curves for operating re-
cords. Record cards for preserving all information regarding each curve.
Xll GRAPHIC METHODS
CHAPTER XIV. RECORDS FOR THE EXECUTIVE 288
Need for complete records in curve form relating to all main features
of a business. Curve-card filing methods. Blueprints from the curve
cards allow a cross-index of all important operating curves. A complete rec-
ord department for a business. Methods for keeping records as used by
various large corporations. The need for education in the interpretation of
curves. Curves in conference meetings by using a reflecting lantern and
the curve-record cards without lantern slides. Curves on swinging-leaf dis-
play fixtures.
CHAPTER XV. CORPORATION FINANCIAL REPORTS 307
The annual report of corporations not usually put in form to permit
intelligent comparison by the stockholders. Records of previous years
not usually given. The number of stockholders constantly increasing.
Best policy is to give complete and clear information. Recent examples
showing bad practice. Curves for the United States Steel Corporation as
a suggestion for the type of chart to be included in a corporation annual
report. Charts should be a feature of "the annual report of every large
corporation.
CHAPTER XVI. GENERAL, METHODS 321
Methods for collecting and tabulating data. Punched-card sorting
and tabulating machines. Use of tabulating machines for manufacturing
records and for analyses of selling results. The slide rule as^ a great con-
venience. The use and abuse of significant figures. Photographic copying
of charts. Use of the reducing glass. Preparation of copy for the engraver.
The Ben Day process. Charts for two independent variables. Card-board
models. Solid models. The desirability of curves and charts in political
campaigns. The projecting lantern with charts for campaign purposes.
Methods for presenting election returns to large numbers of people. Charts
in parades.
CHAPTER XVII. A FEW CAUTIONS " . . . 344
The importance of clear and accurate titles. Symbols which are easily
remembered. No necessity for plotting curves vertically. Errors resulting
in interpretation of curves if the zero of the vertical scale is not shown on
the chart. The selection of scales for curve plotting. Different impressions
from curves from the same data but with various scales. Optical illusions
which may affect graphic work. A checking list for final inspection of
graphic presentations. Need for standard rules of grammar for the graphic
language. A few suggested rules for graphic presentation. Great ad-
vantages may result if graphic methods are more widely used for portray-
big quantitive facts.
GRAPHIC METHODS
FOR
PRESENTING FACTS
CHAPTER I
COMPONENT PARTS
AFTER a person has collected data and studied a proposition
with great care so that his own mind is made up as to the best
solution for the problem, he is apt to feel that his work is about
completed. Usually, however, when his own mind is made up, his
task is only half done. The larger and more difficult part of the work
is to convince the minds of others that the proposed solution is the
best one — that all the recommendations are really necessary. Time
after time it happens that some ignorant or presumptuous member
of a committee or a board of directors will upset the carefully-thought-
out plan of a man who knows the facts, simply because the man with
the facts cannot present his facts readily enough to overcome the
opposition. It is often with impotent exasperation that a person
having the knowledge sees some fallacious conclusion accepted, or
some wrong policy adopted, just because known facts cannot be mar-
shalled and presented in such manner as to be effective.
Millions of dollars yearly are spent in the collection of data, with
the fond expectation that the data will automatically cause the cor-
rection of the conditions studied. Though accurate data and real
facts are valuable, when it comes to getting results the manner of
presentation is ordinarily more important than the facts themselves.
The foundation of an edifice is of vast importance. Still, it is not the
1
2 GRAPHIC METHODS
foundation but the structure built upon the foundation which gives
the result for which the whole work was planned. As the cathedral
is to its foundation so is an effective presentation of facts to the data.
We daily see facts presented in the hope of creating interest and
action for some really worthy piece of work to benefit the people as
a whole. In many of these cases the attitude of the person presenting
the matter seems to be that the facts will speak for themselves and that
they need little or no assistance. Ordinarily, facts do not speak for
themselves. When they do speak for themselves, the wrong conclu-
sions are often drawn from them. Unless the facts are presented in a
clear and interesting manner, they are about as effective as a phono-
graph record with the phonograph missing.
If it were more generally realized how much depends upon the
method of presenting facts, as compared with the facts themselves,
there would be a great increase in the use of the graphic methods of
presentation. Unlimited numbers of reports, magazines, and news-
papers are now giving us reams of quantitative facts. If the facts
were put in graphic form, not only would there be a great saving in
the time of the readers but there would be infinite gain to society,
because more facts could be absorbed and with less danger of mis-
interpretation. Graphic methods usually require no more space than is
needed if the facts are presented in the form of words. In many
cases, the graphic method requires less space than is required for words
and there is, besides, the great advantage that with graphic methods
facts are presented so that the reader may make deductions of his
own, while when words are used the reader must usually accept the
ready-made conclusions handed to him.
In many presentations it is not a question of saving time to the
reader but a question of placing the arguments in such form that re-
sults may surely be obtained. For matters affecting public welfare,
it is hard to estimate the benefits which may accrue if a little care be
used in presenting data so that they will be convincing to the reader.
If the average citizen, and especially the business man, knew how to
interpret charts and curves, it would be feasible to convey to him in
effective form those facts relating to broad public improvements,
public-service operation, and national, State, or municipal manage-
ment, which might affect the whole fabric of our civilization. Archi-
medes wanted only a fulcrum for his lever and he would move the
world. If the world is ever moved it will probably be by facts properly
COMPONENT PARTS 3
presented. The method of presentation is the fulcrum without which
facts, as a lever, are useless.
The preparation and interpretation of simple charts and curves
should be taught in the public schools as a part of arithmetic. The
work of kindergarten nature now done in the lower grades of the
public schools could very readily be extended so that the pupils would
be making charts and curves without realizing that the work (or play)
had any relation to mathematics. Text-books for geography are al-
ready making effective use of charts. In the public schools of Newark
and of Trenton, New Jersey, grammar-school pupils are preparing
charts and plotting curves relating to records which show the present
condition and recent development of their home city. The principles of
charting and curve plotting are not at all complex, and it is surprising
that many business men dodge the simplest charts as though they
involved higher mathematics or contained some sort of black magic.
If an editor should print bad English he would lose his position.
Many editors are using and printing bad methods of graphic presenta-
tion, but they hold their jobs just the same. The trouble at present
is that there are no standards by which graphic presentations can be
prepared in accordance with definite rules so that their interpretation
by the reader may be both rapid and accurate. It is certain that
there will evolve for methods of graphic presentation a few useful
and definite rules which will correspond with the rules of grammar
for the spoken and written language. The rules of grammar for the
English language are numerous as well as complex, and there are about
as many exceptions as there are rules. Yet we all try to follow the rules
in spite of their intricacies. The principles for a grammar of graphic
presentation are so simple that a remarkably small number of rules
would be sufficient to give a universal language. It is interesting to
note, also, that there are possibilities of the graphic presentation be-
coming an international language, like music, which is now written
by such standard methods that sheet music may be played in any
country.
With oral and written language and with tabulated figures also the
reader sometimes draws conclusions regarding the relative importance
of different things from the comparative length of time or amount of
space used in presentation. Graphic methods overcome this difficulty
by showing quantitative facts in true proportions which give instantly
the correct interpretation. In tabulations like that on page 4 it is only
4
GRAPHIC METHODS
the highly skilled reader who can refrain from regarding the five differ-
ent items listed as of somewhere nearly equal numerical importance,
simply because the five different items are given exactly the same space
and prominence when written down on the page.
PERCENTAGE OF EACH RACE IN THE POPULATION OF THE WORLD
Yellow 45
White 41
Black 11
Brown 2
Red 1
It requires mental concentration in interpreting even these simple
figures to get the correct impression of the very large percentage of
the two chief races and the numerical insignificance of the one last
named. If these data were shown in a simple horizontal bar, somewhat
like that seen in Fig. 1, the relative proportions of the different races
Scale l*«lCeot»
5 Cents
Fig. i. Disposition of a 5-cent Fare Paid to the Boston Elevated Railroad in the Year
Ending September 30, 1909
The horizontal bar gives an especially good method for showing component parts
COMPONENT PARTS
would instantly be seen without any mental effort on the part of the
reader.
Fig. 1 is a very satisfactory form of chart to bring out the component
parts of any group total. The horizontal bar need be made only wide
enough to show the various kinds of shading necessary to give a good
contrast. Engineering dimension lines above each block in the bar are
of great advantage
for convenient read-
ing. The dimension
lines permit of group-
ing in such a manner
that several of the
detail blocks could
be included in vari-
ous sets of dimension
lines to show such
items as total fixed
charges, total operat-
ing expenses, etc.
In this type of
chart the actual
figures representing
the value of the com-
ponents should be
given for the use of
any reader who may
wish to draw his own
conclusions or to
make new combina-
tions of figures dif-
50%
•SALARIES & WAGES
Fig. 2. Disposition of the Gross Revenue of the Bell Tele-
phone System for the Year 1911
This chart was taken from the annual report to the stockholders of the
American Telephone and Telegraph Company for the year ending
December 31, 1911
The circle with sectors is not as desirable an arrangement as the hori-
zontal bar shown in Fig. 1
ferent from those shown in the chart. As a general thing it is always
desirable to have full data given on any chart. Fig. 1 gives all the data
without in any way detracting from the ease of reading the chart itself.
It would be desirable to have a large number of the illustrations
in this book printed in color. Charts which are made in color can read-
ily bring out points which are not easily portrayed when only black ink
is used. The reader should keep in mind for his own work that he
should use colors in making those charts where colors are economically
possible. For the purpose of this book, color printing is prohibitive
6
GRAPHIC METHODS
on account of the cost. In printed reports, in magazine articles, and
in magazine advertising, color printing is not at the present time com-
monly available. The illustrations of this book will accordingly show
what can be done in printing complex charts with only one color of ink,
under the same conditions
that would be found in the
preparation of material for
magazine articles, printed
reports, and ordinary pro-
spectus or other advertis-
ing matter.
Fig. 2 is a form of chart
used probably more widely
than any other form to
show component parts. The
circle with sectors is not a
desirable form of presenta-
tion, however, because it
does not have nearly such
flexibility as the method
shown in Fig. 1 . The sector
method does not permit of
convenient arrangement of
names for the different
components. Note that the direction of the lettering must be reversed
as the eye proceeds around the circle. In this case, "Interest and
Dividends" reads upward while "Materials, Rents, Traveling Ex-
penses, etc." reads downward. Another disadvantage of the sector
method is the impossibility of placing figures in such manner that they
can be easily compared or added. The horizontal-bar method permits
of placing figures so as to keep the decimal points in line, thus making
it possible to add the whole column of figures relating to the various
components.
The sector method is probably so widely known through presentation
in exhibits, illustrations for popular magazines, etc., that it is more
generally understood than any other method now in use. The more
easy reading of the wedge or sector chart is, however, largely due to
habit. If the horizontal-bar method of Fig. 1 were used as frequently
as the sector method, it would be found in every way more desirable
Fig. 3-
The Survey
Disposition of a Family Income of from
$900 to $1000
This cut shows an eltempt to put figures in popular form.
The eye is likely to judge by the size of the pictures rather
than by the angles of the sectors
COMPONENT PARTS
W»T THROUGH BAOtATION, LEAKAGE OF STEAM ETC
LOST THROUGH UNCONSUMED FUEL IN ASH
-
u. 30
O
160
14O
LOST IN VAPORIZING MOISTURE IN COAL
I
lOOj
UTILIZED 6V BOILER
than the sector method and would, in a very short time, become so well
known that it would be read much more quickly and accurately than
the method involving sectors.
In Fig. 4 a double scale is used by which the same data can be
interpreted from two different standpoints. On the left the scale is
given in millions of tons, and on
the right in millions of dollars.
The reader can interpret the chart
from whichever standpoint he
prefers. Though this chart is ar-
ranged vertically instead of hori-
zontally, it really makes little
difference which way the bars are
placed. As a general thing, the
horizontal arrangement lends itself
more readily to the use of type so
that the reader may read type
statements without having to turn
the book.
In Fig. 5 the whole population
of the United States is divided first
into native white, foreign white,
,and colored, then each of these
groups is subdivided according to
place of birth. This is an excellent
type of chart to use if subdivi-
sions in the component parts of
any unit have to be shown. If the
scale to which the chart is drawn
is specified, it is possible for the
reader to measure, with an ordi-
nary ruler or with an engineer's
scale, the exact percentage size of
each of the different components.
If the chart is made on co-ordinate paper with ruled squares, the
reader can obtain the size of each component direct from the co-ordinate
lines. The trouble, however, with using co-ordinate paper for charts
of this sort is that the components are likely to begin and end at points
not falling upon the co-ordinate lines, thus making it necessary to count
';.••:::';'.• ':' . .CONSU MEO UY stAin'iNA fWV v%
KtXPlKA (E»-lSI«e HOT1 WHILE if AHO(M<^ '-
AND LEFT IN FIRE BOJCJCT fTNpO* «yN(EiTA.
Adapted from Data, Chicago
Fig. 4. Utilization and Accompanying
Wastes of One Year's Coal Supply for
Locomotives on Railroads of the
United States
The double scale permits reading this chart in tons
or in dollars
8
GRAPHIC METHODS
fractions of a division at both beginning and end of the component
to be measured. The best thing in charts of this kind is to use unruled
paper, and specify the scale. The reader, if he wants the exact data, can
take his measurements with a ruler. The engineer's scale has its sub-
divisions in decimals and hence is the most convenient scale for chart
work. An engineer's scale should be part of the equipment of every
person who has charts to make.
Another method of showing the relative size of the divisions and sub-
divisions of a unit or group is shown
in Fig. 6. In this case we have the
total population of the United States
split into its component groups accord-
ing to the condition in regard to mar-
riage. The subdivision bars, given be-
low the total bars, show the conjugal
condition in each of the main groups
which enter into the total population.
Each of these main-group bars is cross-
hatched to show the conjugal condition
within the group. The combined length
of the four bottom bars is equal to the
length of the total-population bar
shown at the top. These same data
could have been presented by the
method shown in Fig. 5. It will be
noted, however, that in Fig. 6 all the
figures have been included, and are
available for reference purposes with-
out detracting from the utility of the chart itself. The lettering was
done by hand and shows the possibilities for neatness resulting from
hand work when a skilled draftsman is employed. In many ways the
method of Fig. 5 is preferable, but it is probably true that Fig. 6
would be more readily understood by the average untrained reader.
Where there are a large number of items to be compared and the
components of each item are given, the method of Fig. 7 is a very
convenient one. The Census Atlas for the 1900 Census contained
many pages of charts of this type for its comparisons of different States.
By placing bars for all the States on one page, the total for the country
is shown as 100 per cent in the vertical direction. No vertical scale
Scale p0 inch equals 5 percent
United Slates Statistical Atlas for the Census of 1900
Fig. 5. Elements of the Population
of the United States in 1900
Here the components of the total population
are shown in their relative sizes on the
vertical scale. Each component is also
divided into different subdivisions whose
percentage size may be read from the
horizontal scale. This is an admirable
method of presentation if components
must be subdivided
COMPONENT PARTS
SJTAI. POPULATION. .76.3O3.S87
NATIVEorWHITE
NATIVE PARENTS
. . .40.049, 36 Z
FORCION WHITE 10,213.617
SINOLC
MARRIED
WlDOWEO
DIVORCED
Fig. 6. Conjugal Condition of the Population of the United States in 1900
The four lower bars show components of the total population represented by the upper bar. The combined
length of the four lower bars equals the length of the upper bar
is used, all the bars being made of equal width. In this particular
case (Fig. 7) we have a total split into its components and again sub-
divided so as to show the prevalence of a second factor which is in-
cluded in the first. Thus, we see the proportion of illiterates in each
of the main groups of population for each State. All of the States
are shown on the same basis, since all are depicted by bars of the same
length representing 100 per cent. It is not easy to make a clear black-
and-white drawing if one kind of cross-hatching must be placed on
top of another kind. Fig. 7 shows that it is possible, however, to
superimpose two kinds of cross-hatching and get a drawing that
is fairly clear. The facts in this chart would have been brought out
better if colors had been used for the main divisions of population.
Ruled cross-hatching in black to represent the percentages of illit-
New York
60%
North Dakota
57.8%
West Virginia
83. 2 °/0
Mississippi
Illiterate
Fig. 7. Males of Voting Age in certain States, in 1900, by Color and Nativity and
by Illiteracy
A method for two successive divisions into components is shown here. The proportion of illiterates in each
group is brought out by the horizontal ruling
T«rr I90B.
crates would show clearly through
the colored ink used for the main
divisions.
Though it would have been
possible to portray the data given
in Fig. 7 in the form of the square
shown in Fig. 5, the square would
take up so much room on the page
that the method would be prohib-
itive if all the States had to be
shown on one page for comparison.
With the method of Fig. 7, it is
possible to place on one page all
the forty-eight States so that com-
parison between States can be
made instantly and accurately.
Fig. 8 shows another method of
analyzing to 100 per cent in each
of two directions. The method of
Fig. 5 could be used for these data,
but would not be as easy to under-
stand as the method of Fig. 8.
Fig. 5 would require most careful
cross-hatching to bring out the ver-
tical subdivisions for each of the
different States. By using the
method of Fig. 8, each State can
be shown distinctly even if it is
only the width of a line, as in the
case of Nevada or Wyoming. The
wide space between the different
bars showing the States adds tre-
mendously to the clearness of the
diagram. The vertical scale for
the width of bars is made accord-
ing to the number of electoral
votes from each of the States.
New York has more electoral votes
than any other State, and is there-
10
VER
ME:
DOTTED 'LINE. DIVIDES©
CENTAGE' TO THE. LEFT, BRYAN
HEAVY LINES DIVIDE. ® PAR
FROM THE. LEFT. TAFT, ROOS1
RE.P. PR
V//////////A
S IN I9O8,TAFT PER-
TO THE RIGHT.
IE.S IN 1912.- BEGINNING,
VE.LT. WILSON.
>G. DEM.
Prof. Irving Fisher in the New York Times
Fig. 8. The Vote for President in 1908
and in 1912 by States
Compare this with Fig. 5 where the vertical scale
is continuous, without the gaps necessary here
m order to distinguish different States.
COMPONENT PARTS
11
fore given greater width than any other State in proportion to the
greater size of its electoral vote. The horizontal division has been
made according to the percentage number of votes for each of the
main political parties. Two different elections are shown by using
solid lines and dotted lines. The chart proves that the Democratic
vote of 1913 was essentially the same as the Democratic vote in 1908,
and that a Demo-
crat was elected
President in 1912
largely because
there were three
candidates in 1912
and only two in 1908.
This is an admirable
piece of presentation
even though the
lettering and draft-
ing are not quite as
good as they might
have been if more
care had been used,
though probably al-
lowance must be
Fig. 9. The Factors Entering into the Annual Cost of made for the limita-
Motor Trucking Service P ,
The scheme of this convenient form of tabulation is somewhat similar
to that of Fig. 5. Here, however, the components are only named preSSWOrk in daily
without denoting their relative size or importance . .
newspaper printing.
When studying a number of varied components, and the relations
of each to every other one, a chart like Fig. 9 is frequently of great
assistance. This chart shows that certain components are affected by
features which may not affect other components. We have here the
total cost of motor trucking, studied according to the components of
the cost and also according to the conditions which produce those
component costs. We may consider either the service conditions or
the cost components. We have 100 per cent in the horizontal direc-
tion and 100 per cent also in the vertical direction. The total of the
components in either direction is 100 per cent, but the actual size of
each is not given because the size is not known or because it may
vary from time to time.
Relations Between Annual Cost of Motor Trucks
And Characteristics of Service.
E
!-
—
~a
I
e
t~.
«
a
1
5
s*
I
1
K
I
1
K
•o
•a
Amortization or DepreclAtlon
Interest
Insurance
z
H
V|
'o
B
•3
<
a
I
£
3
J
I
3
•3
C
3
>_
3
a) Character of work:
X
X
X
X
X
X
I
I
Ir
X
X
X
d r
rt re
c 5
c y
X
I
X
X
X
«s
IS
T
X
X
1 it
t il
X
X
lit
lie
X
X
X
X
111
m :
X
X
Iffor
Iffer
X
X
X
X
X
X
ts-c
8 d
X
X
X
sta
istn
X
X
HOP
ice
X
Number of stops per day ....
b) Roads and climate:
Climate
c) System of operating:
Loading and unloading
OverRDeedlnar
Massachusetts Institute of Technology — Vehicle Research
GRAPHIC METHODS
P^ g
O 1
11
IH -f.
<D b
tS -2
d- o
.5 0
co .2
IH 55
^ :>
« -a
03 . C1
H
° 1
co 01
•
o S3
•
o
-
60
COMPONENT PARTS
14
GRAPHIC METHODS
s se
"3J3 2
31
•s s
]c
jje-E
M*
Jl
<3«
I 1I!N l!«N |_J Sog ii»u
inre I«N I I ss°n uiw I
2 — 1 I . J
HaT*Ut I] HIM «!M I
I I ^2 — i_H — I
I lure »•"!» I j IHK "iii I
tlUK Snmoa I _| 1IIK Snpaooi
idna >q8im |~ |«l»aH *""! J"
COMPONENT PARTS
15
STOCKHOLDERS
BOARD OF DIRECTORS
f SECOND VICE PRESI-
ENT AND SECRETARY
cb til ti rh rh r*n
BOOKKEEPERS ,
FIRST VICE-PRESIDENT
TREASURER
1 ASSISTANT TREASURER
ACCOUNTING
1 CHIEF CLERKJ | CHIEF CLERK | [ACCOUNTANT*)
GENERAL SUPERINTENDENT
(MAKING)
SHIPPING
DEPARTMENT
(SALES DEPARTMENT!
| MANAGER 1
1miftl^rIirtujT?^rI^TTtu]T?i 1 1
j »D»EiJT,.,Na cbbubbdd 66^66
CONSTRUCTION AND,
MECHANICAL
DEPARTMENTS
1
[
FINISHING
DEPARTMENT
1 PATTERN MAKING- MOLDING AUfpLA-
NG STEEL RANGE! 1 MOUNTING
ING MAKING ] [(ASSEMBLING)
^L^&cpfe
r|~i ro«s.EN[^3 rh rot™
'EN | | | fAREii
66d] 6 til* b
TTT . i"TT|T T
Y"^CT@Y^
] * atiltiltblti ti6
INSPECTORS
1 1 1 1 1 1 1 1
cbcbiinb cb i± cb cb DcicbanananDacba
WORKMEN WORKMEN WORKMEN
System
Fig. 13. Organization Chart of a large Company Manufacturing Stoves
A complete organization chart should always include the stockholders and the Board of Directors as shown
here
A diagram like that of Fig. 10 may be of considerable assistance
if a very complex relation of components has to be shown. In Fig. 9,
the components have only one subdivision. In Fig. 10, however,
we have fuel cost subdivided as many as five different times. Though
the method of Fig. 10 could easily be used for the data of Fig. 9, that
of Fig. 9 has its advantages in that it makes printing cheaper and
is therefore desirable whenever it can be used. Fig. 9 can be prepared
on a typewriter or can be set up by any printer, while Fig. 10 requires
the making of a drawing.
In Fig. 11 the ramifications of the influence of the J. P. Morgan
Company and various large banking concerns are shown. This chart,
taken from the Pujo Money Report, was drawn originally in several
different colors of ink. Though the windmill effect of the chart is
rather disagreeable to the eye, the chart nevertheless shows the ap-
plication of the graphic method to such complex situations as it is
almost impossible to portray with language alone.
Organization charts are not nearly so widely used as they should
be. As organization charts are an excellent example of the division
of a total into its components, a number of examples are given here
in the hope that the presentation of organization charts in convenient
form will lead to their more widespread use.
16 GRAPHIC METHODS
It has been well stated that an organization chart closely resembles
a genealogical tree.
Authority reaches down through the several branches of an organization like
descent of blood, and, if properly planned, it will be as irregular for a factor in an
organization to be in doubt as to the person in authority over him as for the child
to deny the parentage of his father. Such a chart should be drawn for every or-
ganization, even more especially for those organizations which are short-handed ex-
panding businesses in which one man holds the authority of several positions. It should
be graphically shown what positions are only temporarily filled, so that when new men
are engaged they will fit into the scheme with functions planned. Then there will
be no irritation, no feeling on the part of some that their authority has been usurped.
If such a chart is made there will be fewer cases of conflict or of short-circuiting
of orders. Every command from the general that is given directly to the private
over the head of the captain weakens the authority of the captain over the private
and weakens the authority of the general over the captain. A military organization
is so planned that each man knows from whom to take orders, but business proceeds
too much on personal authority. An organization chart will help to prevent this.
Of course, no two businesses can have identical organizations. The skeleton
may be the same, however, and just as the proper study of the functions of the human
body begins with the skeleton, so the study of organization should begin with those
simple outlines which appear, in the main, in all completely and successfully organ-
ized businesses. Very few enterprises are organized properly. Very few have an
organization that can be charted at all. That is one reason why there is such in-
efficiency in industry.
As a general thing it is better to have an organization chart begin
with the stockholders and then show the board of directors as inter-
mediate between the stockholders and the president. In reality, a
typical organization chart represents the shape of an hour glass or a
double funnel, with the large number of stockholders on one side and
the large number of employees on the other. The board of directors,
the president, and the officers of the company are at the narrow part,
with the president as the intermediary through which all transactions
take place between the large number of stockholders and the large
number of employees.
The routing of work through the many processes and departments
of a large plant is a subject of such great importance that charts are
frequently desired for the study of such routing. Fig. 14 is a fairly
good example of this class of chart. In a complete chart, the depart-
ments would of course be designated for easy reference, by names,
numbers, or letters. Colored ink could bt used to keep one class of
work distinct from another. Colored inks would help tremendously
COMPONENT PARTS
17
The Engineering aragazine
Fig. 14. Graphic Representation of Processes and Routing in a Representative Plant
Names of departments and operations are omitted by request of the proprietors of the establishment in
which this chart was made
18
GKAPHIC METHODS
w • ? /v — — '•' ' —
f'v ^f .1 Y — ^"^b — e^-^ !
COMPONENT PARTS 19
in simplifying Fig. 14, but are not available here because of the pro-
hibitive expense of color printing. Colored drawing inks can be ob-
tained at almost any stationery store. A bottle of each color should
be a part of the equipment of any person who is regularly doing chart
work. Note in Fig. 14 the small curves drawn where one route line
crosses another line. By means of small curves like these it is very
easy to keep the lines separate and to show clearly that the lines
crossing each other are entirely independent.
Orders and other printed forms sent through a large organization
must follow a routing entirely distinct from that actually followed
by the heavy materials. The routing of printed forms in a large
business is, in itself, a matter worthy of most careful study to get a
true understanding of their complex movements. A clear idea of
office system is almost impossible unless the data are charted. Fig. 15
may give some suggestions for a chart to show the movement of printed
forms through an industrial plant. Here again printing by colored
inks such as would be used on the original drawing would be of great
service in making the chart easy to understand and easy to follow from
department to department.
If a building contains many stories the routing diagram for mate-
rials and also the routing diagram for printed forms can be made
conveniently by a rough perspective drawing showing the different
floors as planes one above the other. Colored ink lines on the
perspective chart will show clearly the movement of materials through
the manufacturing building, and will indicate the elevator movements
for material in a manner not possible if the departments are repre-
sented all in one plane on the ordinary sheet of paper. Perspective
charts of floors, one above the other, are so simply made that their
advantage should not be overlooked when preparing routing charts
for plants having multi-story .buildings.
CHAPTER II
/
SIMPLE COMPARISONS
ONE of a business man's chief assets is his ability to show things
to others in their true proportions. He is continually making
contrasts, and holding up for comparison different propositions
which come up in his daily affairs. The graphic method lends itself
admirably to use in making comparisons. It is surprising how much
clearer even simple comparisons of only two or three items will appear
when their numerical value is put in graphic form rather than in figures.
Fig. 16 is a cut taken from the report of the Metropolitan Sewage
Commission. Most people know so little about bacteria that it would
mean nothing to them to say that the Harlem River contains 15,600
bacteria per cubic centimeter of water. When, however, such a com-
parison is made as is shown in Fig. 16, even the most casual glance
would convince anyone that the Harlem River is not the most ideal
BACTERIA PER CUBIC CENTIMETER OF WATER
ISO I.6OO I5.GOO
ATLANTIC LOWER HARLEM
OCEAN NEW YORK RIVER
BAY
Fig. 16. Bacteria in the Waters of New York Harbor
This illustration is taken from the ~eport of the Metropolitan Sewage
Commission. The representation as though seen through a micro-
scope is decidedly effective
swimming place. The figures for the bacteria count are given with
the chart so that all the data are available to anyone who may wish
to study the facts from a scientific standpoint.
The drawing of Fig. 17 is of the cartoon type, effective for wall
exhibitions or for use in the more popular magazines. This particular
20
SIMPLE COMPARISONS
The Independent
Fig. 17. Five Forms of Our National
Waste
A cartoon type of chart like this will reach a
popular audience. Accuracy of statement
should not, however, be sacrificed as it has
been here, in that there is no way of correctly
comparing the money bags
diagram contains nothing by which accurate comparison may be made.
No figures are given, and it is impossible to tell whether the different
money bags should be compared on
the basis of diameter, area, or volume.
Almost the only conclusion which
can be drawn from such a diagram
is one regarding the relative rank of
the different expenditures. The re-
liability of even that is likely to be
questioned because of the evident
lack of accuracy in this kind of chart.
Nevertheless the cartoonist style
should not be broadly condemned,
for it has tremendous possibilities.
It is possible to combine the car-
toonist's wonderful power of arous-
ing interest with methods of present-
ing facts which will give a numerical interpretation that cannot be
misunderstood. There is a great oppor-
tunity waiting for the man who can
combine cartoon methods with accuracy
of numerical statement.
Fig. 18 gives a statement which the
illustration does not support. In the
first place, the dates of the two years
compared are not given. In the second
place, it is impossible for the reader to
tell whether the diagram is drawn on the
basis of one dimension, two dimensions,
or three dimensions. It would be a hope-
less task to fit the area of the smaller
washing machine into the area of the
larger washing machine. Methods like
this cannot be too severely condemned.
Commercial geography, as it is now
widely taught in the public schools by
listing the various imports and exports of
countries and the products of different
cities, fails to give a clear idea of the
The sale of washing-
machines has increased
sevenfold in the past
three years.
Good Housekeeping
Fig. 1 8. Illustration Intended to
Show that the Sale of Wash-
ing Machines has Increased
Sevenfold hi the Past Three
Years
In comparing the two pictures it is not
likely that the reader will obtain a
ratio of seven to one. There is no
way for the reader to tell on what basis
the drawing was prepared, whether by
height, area or volume. The title of
this chart is also poor in that it does
not name the two years for which the
comparison is made
GRAPHIC METHODS
United States
11,483,000 Bales of 500 Ib
relative importance of the materials listed. It frequently happens that
the second or third item on a list may have only one-tenth the impor-
tance of the first item. Because the three names are given one after
the other, the pupil is quite likely to consider the three items of equal
importance, just as three
persons may be of differ-
ent height, yet of about
the same importance.
The graphic method judi-
ciously applied to school
geography and to general
commercial geography
India
3,082,000
Egypt Russia
1,506.000
900.000
China ,775,000
Brazil 810,000
Fig. 19.
Tan and McMurray's New Geographies
The Six Leading Cotton-producing Coun-
tries in 1910
This arrangement is a bad one to place before school children.
The eye cannot fit one square into another on an area basis so
as to get the correct ratio
would make a tremen-
dous difference in the
student's grasp of the
subject.
Fig. 19 is a typical example taken from a geography book in which
the attempt was made to use the graphic method. The introduction
of the picture of the bale of cotton in Fig. 19 is justifiable. There is,
however, no justification for placing the picture inside of one of the series
of squares. The picture detracts from the size of the square. Graphic
comparisons, wherever possible, should be made in one dimension
only. In such a case as this, one-dimension presentation is perfectly
feasible by the use of bars
of different lengths. The
pupil would find it an al-
most hopeless task to fit
one side of the block for
Brazil into one side of the
block for the United States
and then square the result-
ing ratio in order to learn
that the United States pro-
duces, roughly, thirty times
as much cotton as Brazil.
Bars in one dimension only would show the comparison accurately.
Under any circumstances, the use of the squares of Fig. 19 with the
center line through the centers of the squares gives an extremely poor
arrangement.
1
Tlte World. ~>.
United States
) 2300 5000 7500 jooot
| | 1 1 | 1 1 I 1 | I 1 I | 1 1 1
Indict
The world's produc-
tion of cotton, in 1905, in
millions of pounds.
Dodge's Advanced Geography
rld's Production of Cotton in 1905
Millions of Pounds
Egypt-* -•••
Asiatic Pussia.,n...n
Fig. 20. The We
in
The above illustration together with the title is shown exactly
as given in a recent geography book. Charts like this
greatly assist the pupil in getting the correct relative im-
portance of the different things studied. Note the scale
at the top of the chart
SIMPLE COMPARISONS
VA1TTK OF PHODUCTS FOB PRINCIPAL CITIES: 1909.
CITIES
NEW YORK
CHICAGO
PHILADELPHIA
ST. LOUIS
CLEVELAND
DETROIT
PITT8BURC
BOSTON
BUFFALO
MILWAUKEE
NEWARK
CINCINNATI
BALTIMORE
MINNEAPOLIS
KANSAS CITY, KANS.
6AN FRANCISCO
JERSEY CITY
INDIANAPOLIS
PROVIDENCE
ROCHESTER
LOUISVILLE
SOUTH OMAHA
VOUNOSTOWN
LAWRENCE
NEW ORLEANS
WORCESTER
BAVONNE
AKRON
PERTH AMBOY
LYNN
PATERSON
LOS ANGELES
BRIDGEPORT
FALL RIVER
PEORIA
TOLEDO
OMAHA
DAYTON
LOWELL
VONKERS
ST. PAUL
KANSAS C'TY. MO.
NEW BEDFORD
DENVER
READING
NEW HAVEN
SEATTLE
WATERBURV
HUNDREDS OF MILLIONS
'SO 1000 I
Fig. 21. Value of Manufactured Products of Principal Cities of the United States
in 1909
This chart, taken from a Census office report, would have been greatly improved if the actual figures had
been placed at the left of the bars in the manner shown in Fig. 27
It is stated by the author of the book in which Fig. 19 is used
that tests have shown that children grasp relative quantities better
when separate squares are used than when the information is shown
by lines or bars. If this is the case, it is probably due to the fact
that the squares appear more prominently to the eye than do the bars,
and it would seem that the best kind of presentation might be made
by using much wider bars so that the bars would be easily seen. Bars
can be made as wide as some of the squares seen in Fig. 19 and, if it
seems best, the bars could be made in outline rather than in solid
^4 GRAPHIC METHODS
black. Wide bars would give a striking visual effect and yet they
would vary in one dimension only, so that relative proportions could
be easily judged. Wide bars would probably have all the advantages
and none of the disadvantages of the methods of either Fig. 19 or
Fig. 20. Instead of showing the data of Fig. 19 by either bars or
squares, another method would show pictures of bales in rows of dif-
ferent lengths, on the general scheme of Fig. 41. The rows would be
the same as the broad horizontal bars, but their numerical interpreta-
tion would be less abstract.-
Fig. 20 gives a diagram taken
IS NEWBURGH SATISFIED WITH THIS
SMAU SCHOOL EXPENDITURE?
SCHOOL COST PER PUPIL
NovtoWlel
MtYfcnwnl
flu burn I
ii>..Mrrp»^li^HBBHMi^MHHBBiH '4O.27
-••IMHBBBM^MHHH 139.86
•^••••••^•••M I3G.13
Jamestown •^•••^•••••••H '35.41
Newbuigi ••••••^^•••••i »34.89
Cities 25.000 to 35, 000 People
(JFi£ures based on average daily attendance)
Department of Surveys and Exhibits, Russell Sage Foundation
from another geography book.
This is a much better form of
presentation than used in Fig. 19.
It could, however, be improved by
giving the figures for each country
in connection with its own bar.
Fig. 21 shows the horizontal-
bar method applied to a larger
number of items and proves the
great utility of this method when
several different items must be Fig- 22. Comparison of School Cost per
i ,r . IT Pupil in Cities of 25,000 to 35,000
shown in their proper rank. In Pe£ple ^ New York §££
this Case, however, the figures This iiiustration was photographed down from a
should have been given for the wall exhibit to adapt it to a printed report. The
use of the figures at the right-hand end of the
Convenient USe of any One Who bars is bad practice. The eye is apt to make
. . - , . the comparison from the last figures rather than
might Wish tO make ratlOS Or tO from the ends of the bars
quote the actual value of products
for any one of the cities. It is exasperating to run across a diagram
of this kind which contains valuable information in such form that
it cannot be carried away or quoted for use elsewhere.
In Fig. 22 an attempt has been made to show in the graphic
presentation the figures from which each horizontal bar was drawn.
The method of placing the figures at the right of the bar is, however,
unsafe. The eye is likely to make a comparison, not from the ends
of the bars themselves, but from the right-hand end of the figures.
Since the figures are of about constant length, visual ratios are in-
accurate when made by comparing a short bar plus the constant
length of .figures with a long bar plus the constant length of figures.
If the shortest bar in Fig. 22 were about the same length as the space
SIMPLE COMPARISONS
25
United Kingdom
required for the figures, it would be possible to make a visual error
of 100 per cent in the comparison. If the figures had been placed at
the left of the bars, they would have been in a neat column and not
at all likely to affect the ac-
curacy of the visual com-
parison.
The chart, Fig. 22, was
taken from a report devoted
entirely to the city of New-
burgh. On this account,
it would have been much
better if the word "New-
burgh" had been printed in
heavy-faced type so that it
would stand out from the
other cities in the list.
Where the use of colored
ink is possible, it is fre-
quently desirable to make
the item under foremost
consideration stand out
prominently by giving it a
brilliant color such as red
United States
5O56 : ]
Germany
4..33O
Br Colonies
Vblues given in Thousands
of Tons
Netherlands
SB
Fig. 23. Comparison of the Registered Shipping
of the Principal Countries of the World
The picture at the top of the chart assists in attracting the
attention of the reader. After the attention is gained, the
bars set forth the comparison more accurately than it
could be given by any pictures of ships of different sizes
or green.
Fig. 23 is an attempt to give a popular touch similar to that at-
tempted in Fig. 19 by the bale of cotton. As a general thing, it is
possible to attract attention by some such scheme as the steamship
used in Fig. 23 and then, after the attention is attracted, to give the
comparison by methods which are entirely correct and also familiar
to the average observer. In Fig. 23 the figures are given for the data
from which the bars are drawn. The values, however, were so large
that it was necessary to leave off the last three ciphers and state that
the values given are in "thousands of tons." Though the dropping
of ciphers is very common, it is a practice likely to lead to serious
error and should not be encouraged. Even with the ciphers omitted,
the values could not possibly have been given inside the bar if more
countries had been included in the list, or if the scale had been any
smaller than that shown here. To place above each bar the title for
that bar is not good practice. In general, it is desirable to have a
GRAPHIC METHODS
title for each bar at the left, then the figures, then the bar. With such
an arrangement, one title will be below another, easily perceived by the
eye, and the figures will all be in one column with the decimal points
in a straight line.
Figures running
into millions can be
easily read from long
columns if sufficient
white paper is left
between figures in
UNITED STATES . .493
MEXICO .61
SPAIN a. PORTUGAL .52
JAPAN 42
CHILE 42
AUSTRALIA. .34
GERMANY 32
CANADA . . . .28
THOUSAND! Of TOH»
Production of Copper in Different Countries
for One Year
This chart is a redrawing of Fig. 25. The title here should state the year,
but that was not given in the book from which Fig. 25 was taken
Fig. 24.
the vertical arrange-
ment, and if each
group of three figures in the horizontal arrangement is widely set oft"
by means of a comma. For graphic work, the groups of three figures
should, in general, be more widely set apart than they are ordinarily.
Fig. 24 shows the arrangement with the figures at the left of the
bars. Here again, however, the ciphers have been omitted when it
would probably have been just as clear if they had been included and
set off by means of a comma and a wide space. The drawing for the
pigs of copper
shown at the left
of the illustration
«(«<' gives an idea of
what can be done
by hand drawing
in order to at-
tract attention to
the subject which
the chart itself is
intended to illu-
minate. In this
\ „///„////
\ ..„/,.,;////
\ ...,„//////
X
X
§
X
X
*?
^
^
United States
493,476
Chile Australia Germany Canada
Mexico Spain & Japan
Portugal
61,000 52,188 42,310 42,043 34,339 32,298 28,733
Philips' Chamber of Commerce Atlas CaSC the lettering
Fig. 25. A Year's Production of Copper in Tons
This illustration was copied from a prominent book on international trade.
Accurate interpretation of the chart is impossible. Graphic work of
this sort is dangerous because it may be misleading
also has been done
by hand and is a
good example of
what a skilled
draftsman may do without any great expenditure of time. The solid
black bars of Fig. 24 come out in much better contrast than the gray
bars of Fig. 23.
SIMPLE COMPARISONS
27
Federated Malay
States
68,856
Bolivia
Fig. 25 shows a chart of the same data from which Fig. 24 was
drawn. It is readily seen that it would be impossible for the average
reader to tell whether this chart was drawn on the basis of height or
the basis of area. The pigs of copper are not of the same size in the
different piles, and it is evident that a pictured pig of copper is not
intended to be the unit. If Fig. 25 is drawn on an area basis, it is al-
most impossible for the eye to fit the area for the right-hand pile into
the area of the left-hand pile. This chart is a typical example of
thousands of illustrations used by the popular magazines and even
by some of the more pretentious reference books,
Fig. 26 is an even greater
atrocity than Fig. 25. In Fig.
26, the observer is entirely un-
able to tell whether comparison
is made in one, two, or three
dimensions and he has an addi-
tional puzzle because of the large
amount of perspective shown
for the top of the pigs of tin.
It would be surprising if one man
in a thousand could guess any-
thing near the ratio intended to be expressed between the largest and
smallest pigs shown. In general, graphic work of this kind is much
worse than the use of figures alone. There are times when an ab-
sence of knowledge is better than incorrect knowledge.
Fig. 27 is a good example of what can be done as a standard arrange-
ment for simple comparisons. On the left there is a symbol to attract
the eye and interest the observer.
Note that a dollar mark is shown
on top of the picture of the bale
of cotton in one case and the sheaf
of wiieat in the other, to indicate
that the value of the crop is con-
sidered rather than the number of
Dutch E. Austra- United Siam
Indies lia Kingdom
29,937 15,807 12,755 5,052 3,000
Philips' Chamber of Commerce Atlas
Fig. 26. A Year's Production of Tin in Tons
This illustration, taken from the same source as Fig.
25, is even more confusing. The perspective of
the tops of the pigs of tin is such that there is
no way of telling whether visual comparison
should be made by height, area or volume
COTTON $ ezo.zso.ooo
WHEAT $661,051,000
Fig. 27. Value of Cotton and of Wheat
Produced in the United States in 1910
units AftfM* tnp rnrtnr^ wninn Her,e is a suggestion for a standard arrangement for
UnitS. Alt eS, Wn horizontal-bar comparisons. The illustrations
may be thought of as "eye catch-
ers," we have the figures, and then
the bars plotted to scale for quick comparison by the reader. This
cut could have been improved slightly if the spaces between the sep-
horizontal-bar comparisons. The illustrations
at the left make the presentation popular in
form, yet actual figures for the data are given
at the left-hand end of the bars
GRAPHIC METHODS
arate groups of three figures had been made somewhat larger and if
the black bars had been made about one and one-half times as wide
as shown here.
TOTAL POPULATION
SINGLE
MARRIED
WIDOWED
DIVORCED
SINGLE
MARRIED
WIDOWED
DIVORCED
SINGLE
MARRIED
WIDOWEP
DIVORCED
SINGLE
MARRIED
WIDOWED
DIVORCED
NATIVE WHITE OF NATIVE PARENTS
NATIVE WHITE OF FOREIGN PARENTS
FOREIGN WHITE
NEGRO
SINGLE
MARRIED
WIDOWED |
DIVORCED
w
m
Untied States Statistical Atlas. 1900 Census
Fig. 28. Status of the Population of the United States in 1900, in Regard to Marriage
This chart would have been improved if the figures had been given at the left «nd of the bars. Note that
the four lower groups of bars are a cross-index of the information given in the upper group
Another application of the bar method is seen in Fig. 28. Each
of the four lower groups of population is a subdivision of the total
population shown in the upper group. The same data may be
seen portrayed in a different way in Fig. 6. The arrangement of
Fig. 6 is more desirable, in that the size of the components is more
readily grasped when all are shown in the same horizontal bar. In
Fig. 28 the eye does not readily make the addition necessary to fit
together the four items "Single," "Married," "Widowed," and
"Divorced" as percentages of the total 100 per cent in each group.
The drawing in Fig. 29 is a portion of an illustration intended
to show how far different kinds of trucks could travel for an expend-
SIMPLE COMPARISONS
iture of one dollar. The placing
of these trucks on different levels
is somewhat confusing, but it was
done in order that one truck would
not have to be shown back of an-
other. Note the bars behind each
truck, to give the component parts
of the total expenditure split into
different kinds of charges. This
chart is grossly misleading because
the point where the race started
is not shown. It appears, for in-
stance, that for one dollar ex-
pended a five-ton gasoline truck
will run about twice as far as a
five-ton horse truck. This con-
clusion is entirely unwarranted,
and would not be reached by any
reader if the chart had been so
drawn that the zero point or
starting point for the race had
been shown to scale at the left
end of the chart.
The black bars used in Fig. 30
to show contagious diseases indi-
cate an excellent method for differ-
entiating items shown in graphic
comparison. In the Boston health-
report illustration from which this
cut was adapted, the infectious
diseases were shown in red. By
making most of the bars in outline
only, it was possible in Fig. 30 to
use solid black to get the contrast
obtained in the original report by
means of red ink.
It is frequently necessary to
show increases and decreases on
the same chart so that they may
30
GRAPHIC METHODS
1,300
1.200
1.100
1,000
900
800
700
600
500
400
300
200
100
III
Ia If ... i -if 1 Hi -
*f fis I |&|?! ss I** -I I
^B Drathi from Infectious Diieun.
CTZ) DMttw from other DiiMuu,
Annual Report of the Health Department, City of Boston, 1910
Fig. 30. Comparative View of Twenty-
five of the Principal Causes of Death
hi Boston During 1910
In the Boston report, the infectious diseases were
represented by red bars. Here attention is called
to the infectious diseases by using solid black
bars in contrast with bars shown only in outline
zero line. The figures can be
placed on the left-hand margin
of the chart, immediately between
the title for each bar and the end
of the bar, in a manner similar to
that shown in Fig. 27. Since the
zero line must be near the center
of the chart, rather than at the
left-hand edge, when the right-
and-left arrangement is used, it
be in contrast. In Fig. 31 an ex-
ample of the contrast of increases
and decreases is given, increases be-
ing shown to the right of the zero
line and decreases shown to the left
of the zero line. This right-and-
left arrangement of increases and
decreases is fairly well known and
is so convenient that it should be
more widely used. The actual
figures from wrhich each of the hori-
zontal bars is drawn can be shown
on the chart even if the horizontal
bars are drawn to the left of the
REPAIRS AHD REF1EWAL3 Or LOCOHOTIVES
PER TOn TRACWE FORCE.
Average of 6 Years Ending 1910 Compared
with 4 tears Ending /9O5.
\ %ffKR£A3E.
f
MJcW
&*o.
LV.
CSI.&STP.
&?./.**
c.tnw.
WROMS. I
WESTERN 'ROWS.
"Railroad Operating Costs," Suffern & Son, New York
Fig. 31. Increase is Here Shown to the
Right of the Zero Line and Decrease to
the Left of the Zero Line. A Heavier
Zero Line and Arrows Pointing Right
and Left from it Would Improve This
Chart
SIMPLE COMPARISONS
would be well to have a broad line for the zero line, so that the
eye may at once perceive that zero is not at the left-hand edge of the
chart. It would have been better if the zero line in Fig. 31 were some-
what broader. Another help to the reader could be given by placing
an arrow pointing to the right with the word "increase" and an ar-
row pointing to the left with the word "decrease."
Transformers
Transmission Line
Transformers
Notary Converters \
Contact Line
Power Delivered
to Locomotives
Journal Amer. Soc. Mechanical Engineers
Fig. 32. Comparative Losses Between the Power House and Locomotives with Differ-
ent Systems of Electric Traction
The comparison of the losses in the different power systems is very clearly shown in this illustration, which
was taken from a paper by George Westinghouse
Broad bars can be used either vertically or horizontally. The hori-
zontal arrangement is usually the more convenient, as it lends itself
more readily to the use of type and horizontal lettering for the titles,
data, etc., of each bar, without forcing the reader to turn the book
at right angles. In Fig. 32, however, the lettering can perhaps be
more conveniently grasped by the reader with the bars placed ver-
tically instead of horizontally.
Note the lines connecting different bars to show how the com-
ponents compare in size therein. These lines assist greatly in giving
a clear and rapid interpretation of the chart.
Fig. 33 is an admirable example of what the graphic method can
do to boil down complex facts for quick interpretation by the reader.
In this case the schools of each of the forty-eight United States were
TEN TESTS OF EFFICIENCY
t. WASHINGTON
2. MASSACHUSETTS
3 NEW \ORK
4 CALIFORNIA
5 CONNECTICUT
6 OHIO
7 NEW JERSEY
8 ILLINOIS
9 COLORADO
10 INDIANA
I \ RHODE 15LAND
12 VERMONT
13 NEW HAMPSHIRE
14 UTAH
15 OREGON
16 MONTANA
17 MICHIGAN
18 N DAKOTA
19 IDAHO
£0 MINNESOTA
H IOWA
22 MAINE
& PENNSYLVANIA
iA KANSAS
25 NEBRASKA
&> 5. DAKOTA
£T NEVADA
Z8 WISCONSIN
^ WYOMING
30 ARIZONA
31 OKLAHOMA
5Z MISSOURI
33 W VIRGINIA
M FLORIDA
35 DELAWARE
56 MARYLAND
37 TENNESSEE
38 TEXAS
39 LOUISIANA
40 NEW MEXICO
41 VIRGINIA
42 KENTUCKY
45 ARKANSAS
44 GEORGIA
45 MISSISSIPPI
Af> N.CAROLINA
4? 6- CAROHNA
49 ALABAMA
V//////WMMAV//////AV////M
'///////A i m
i i
Fig. 33. Rank of States in Each of Ten Educational Features, 1910. White Indicates
that the State Ranks in the Highest 12 of the 48, Light Shading that it Ranks
hi Second 12, Dark Shading that it Ranks hi Third 12, and Black that it Ranks hi
Lowest 12
The above illustration is a photograph of one page of a pamphlet issued by the Division of Education of
the Russell Sage Foundation, regarding the public schools of the United States. This type of chart is
capable of wide application in other fields
32
SIMPLE COMPARISONS
33
considered from each of ten different view points. The different
States were then arranged in grades one, two, three, or four, according
to the efficiency of their schools from each of the ten different points
of view from which they were considered. The best grade under
each heading is shown by means of a white rectangle, the second grade
by light cross-hatching, the
third grade by dark cross-
hatching, and the fourth
and worst by solid black.
States are shown in the
complete chart in their com-
parative rank. The State
with the best schools is
shown at the top of the
chart and the State with
the worst schools is shown
at the bottom of the chart.
On the chart as a whole,
one can see at a glance just
how the schools of any State
rank with those in the
other States, and wherein
the greatest defects occur.
The chart of Fig. 33 was
in a thirty -page illustrated
pamphlet sent broadcast
over the United States by
the Russell Sage Founda-
tion to members of various
legislatures, school boards,
etc. This pamphlet has
resulted in the appropriation
Fig. 34. Organization of the United States
Adjutant General's Office Compared with
Organization Proposed by President Taft's
Commission on Economy and Efficiency
This method of connecting blocks with lines to show the dis-
position of departments can be used in many types of
chart presentation
of some millions of dollars for the
improvement of public schools. The arrangement of the pamphlet
itself is worthy of note in that each left-hand page is a chart, while
each right-hand page, facing the chart, is devoted to a brief explana-
tion of the conclusions which can be made from a study of the chart.
This arrangement of alternate pages of chart matter and printed matter
is tremendously effective and is well worth copying.
It is frequently necessary to contrast one grouping of components
34
GRAPHIC METHODS
with another grouping of components. In Fig. 34 we have a chart
which may give a valuable suggestion to anyone who is considering
the rearrangement of departments in any large organization. The
present arrangement and the proposed arrangement are each clearly
indicated, with connecting lines to show instantly the disposition of
each of the old departments.
EnlhteJ
Men'* Di-
vision
Adjutant
Cenenil
Explanation.
Steps under present
I. Receives.
•2. Drafuniemorun
dum.
3. Transmits.
•I. Delivers.
5. Re eel ves and
Irutisniiis.
6 Receives.
T Examine:
8 Dru fls report
9. 'I r:insmii>
10. Review*.
11 Tr;insmits
12. Helivers.
13. Exjj.iines.
H. TmtumlU
15. Delivers
I'j Examines
17. Indorses.
M. Delivers.
19. Approves
20. Delivers.
21. Indorses.
22. Delivers.
2:1. Exumines.
21. Reviews.
25 Drafts order
26. Types order.
27-fiecordsuttibn
28. Kxnmincs.
-•9. lull inls.
so. Throws in "out,1
box.
:il Collects.
:«. Tninsiniis
:«. HHiu-n.
31. SiKll«.
:(.'.. IVIiv.-r-.
:u; Not.'* I inn'.
:i7. Kxnmliit*.
:«. Wrili-s ciinl.
:!'.). PisiHilrlicV
Steps under
projKised system
! c.V.1 II IT five
ri.rrrsiionil-
rin ml draft.*
onlrr.
2 (•-".') R i> view*
nnil initials.
:t CM) Throws
in "mil" hox.
Fig. 35. Routing of a Letter Through the Adjutant
General's Office Requesting the Discharge from the
Army of an Enlisted Man hi Recruiting Service,
Contrasted with the Routing Proposed by President
Taft's Commission on Economy and Efficiency
By referring to the horizontal scale and to the vertical scale the steps
can be studied either by departments or by operations
In Fig. 35 is given a convenient method to show the routing of
papers through a large office, together with the operations through
which these papers must pass. Across the top of the chart is a scale
of departments. The circles drawn immediately below the space for
SIMPLE COMPARISONS 35
any department on the upper scale show that the papers receive some
action in that particular department. At the right is a scale showing
the nature of the work done in each of the departments. The chart
is drawn on the basis of the intersection of vertical lines downward
from the names of departments and horizontal lines through the
names of the operations given at the right. Arrows joining the various
circles then give the routing of the papers through the whole of the
journey. The comparison of the existing routine with the proposed
routine can be seen by considering the solid lines and the dotted lines
and by comparing the two distinct columns or lists at the right. Thirty-
nine operations may be counted in the present arrangement against
five operations in the proposed arrangement. Though the drafting
and the detail arrangement of this chart could be improved, the gen-
eral scheme is nevertheless worthy of attention.
CHAPTER III
1900
1850
THOUGH in making comparisons, the horizontal bar divided into
blocks is superior to the circle divided into sectors, the circle
and sector arrangement is not inaccurate when only the com-
ponent parts of any unit are to be shown. In the case of Fig. 36, how-
ever, the comparison is between two circles, the divisions into com-
ponent sectors being only an incidental
feature. In this diagram, copied direct from
the Statistical Atlas of the 1900 Census, it
is practically impossible to tell how much
larger the foreign-born population was in
1900 than it was in 1850,
for it is necessary to com-
pare the two circles on an
area basis. To the average
person this is an almost
impossible task, because it
is not feasible to fit one
circle inside of the other
visually as two horizontal
bars may be fitted. If the
circle for 1900 were esti-
mated as twice the diameter
of the circle for 1850, it
would mean that the for-
eign-born population
Irish
Germans
British
IV\V;*.ViVJ Canadians
Scandinavians
Slavs
l\\Vn\\1 Italians
fcyffv^ All Others
United States Statistical Atlas, Census of 1900
Fig. 36. Foreign-born Population of the United
States in 1850 Compared with that in 1900,
also the Proportion of the Different Nation-
alities hi the Two Years Compared
in
The method of presentation by means of a circle with sectors
is not inaccurate when only component parts are to be
shown. Here, however, we have two different circles com-
pared on the basis of total area. The reader cannot com-
pare the areas visually so as to get the correct ratio meas-
ure of the increase in total number of foreign-born popula-
tion. Horizontal bars are much preferable to circles when
comparisons are to be made
1900 was four times as great
as that in 1850. If, how-
ever, the ratio were some-
thing less simple than this,
interpretation of the chart would be difficult even by the processes
of mental arithmetic. If the ratio between the diameters were,
COMPARISONS INVOLVING TIME
37
1910
for example, one and a half, the average reader would be completely
nonplussed, as he would not trouble to go through the mental arith-
metic of multiplying one and a half by one and a half. In general, the
comparison of two circles
of different size should
be strictly avoided.
Many excellent works
on statistics approve the
comparison of circles of
different size, and state
that the circles should
189O
1900
1,647 2,244 3.3O2
Figures in Millions of Dollars
Fig. 37. Total Yearly Value for the United States always be drawn to rep-
of Combined Imports and Exports by Land and resent the facts on an
by Sea
In this illustration the data have been represented by circles
drawn on a diameter basis. The right-hand circle appears
more prominent than the data would justify. Circles com-
pared on a diameter basis mislead the reader by causing him
to over-estimate the ratios. Compare Fig. 38
area basis rather than on
a diameter basis. The
rule, however, is not al-
ways followed and the
reader has no way of telling whether the circles compared have been
drawn on a diameter basis or on an area basis, unless the actual
figures for the data are given so that the dimensions may be verified.
In Fig. 37 the figures
are given, and the circles
have been drawn on a
diameter basis. It will be
noted that the figures for
1910 are roughly twice
those for 1890. Thecircle,
however, has roughly four
times the area of the circle
for 1890 and, according-
ly, seems to have much
more than twice the im-
portance. In Fig. 38, the
same data . have been
shown on an area basis
1890
190O
1910
U647 2,244 3,302
Figures in Millions of Dollars
Fig. 38. Total Yearly Value for the United States
of Combined Imports and Exports by Land
and by Sea
Here the data of Fig. 37 have been shown by means of circles
drawn on an area basis, as recommended by many authorities
on statistical work. The right-hand circle, however, shows up
less prominently than the figures would justify. Circles com-
pared on an area basis mislead the reader by causing him to
underestimate the ratios. Circles of different size should never
be compared. Horizontal bars have all the advantages of
circles with none of the disadvantages
as most of the authorities on statistical
work recommend. If the figures were not given, the reader would be
forced to fit the left-hand circle into the right-hand circle on an area
basis, or else make a ratio between the diameters and then square the
ratio. Either process is almost impossible to accomplish and there is
38
GRAPHIC METHODS
MINISTRY
LAW MEDICINE EDUCATION BUSINESS PUBLIC SERVICE
8
£
T
to
o>
00
MINISTRY
LAW
MEDICINE EDUCATION BUSINESS PUBLIC SERVICE
Independent
39- Proportion of College Graduates in Different Professions in 1696-1700 and
in 1896-1900
Charts of this kind with men represented in different sizes are usually so drawn that the data are represented
by the height of the man. Such charts are misleading because the area of the pictured man increases more
rapidly than his height. Considering the years 1696-1700, the pictured minister has about two and one-
half times the height of the man representing public service. The minister looks over-important because
he has an area of more than six times that of the man drawn to represent public service. This kind of
graphic work has little real value
no necessity of inflicting such cruelty on a reader. Though the circles
in Fig. 37, drawn on a diameter basis, exaggerate the ratios, the circles
in Fig. 38, plotted on an area basis, make the reader underestimate
the ratio. Comparison between circles of different size should be
absolutely avoided. It is inexcusable when we have available simple
methods of charting so good and so convenient from every point of
view as the horizontal bar.
In Fig. 37 and in Fig. 38, it would have been better if the year
had been given under each circle, with the figures for quantity placed
above the circles, so as to follow the standard arrangement of having
COMPARISONS INVOLVING TIME
39
1911
1899
H.59 1,000
One Mite
32,837,000
One Mile
dates placed always at the base of
the chart.
Another difficulty in the com-
parison of areas is shown in Fig.
39. No figures have been given
and the helpless reader must com-
pare by means of the pictures
alone. By measurement, it will be
seen that the minister in 1700 has
over three times the height of the
minister in 1900. Since the man
in each case is shown in his natural
proportions, the picture of the
minister in 1700 has over nine
times the area of the picture for
1900. Whether the ratio should
be roughly three or roughly nine,
we cannot tell.
Another example of the same
kind of difficulty appears in Fig. 40,
but here the figures are given and
we can check up the author to see
whether he has drawn the 1911 man on the basis of height or on the
basis of area. The 1911 man, on account of his far greater area, looks
to be rather more than two and a quarter times as important as the
man of 1899. Though this type of graphic work is quite common, it
should be avoided, for its visual inaccuracy is serious enough to cause
distrust of the whole graphic method. In considering Fig. 40, the point
14.591,000
ONE MILE
World's Wort
Fig. 40. Passengers Carried on the Rail-
roads of the United States hi 1899
and in 1911 Compared
This illustration has all the bad features mentioned
for Fig. 39. Here the numerical data are given
and we can prove for ourselves that the two
pictured men are compared on the basis of
height. Because of the disproportionate area,
the right-hand picture gives the reader a false
and exaggerated impression of growth. See
Fig. 41
1911
32,837000
ONE MILE
Fig. 41. Number of Passengers Carried on the Railroads of the United States in 1899
and hi 1911 Compared
Here is a chart drawn from the same data as Fig. 40. It was not a larger passenger, but more passengers,
that the railroads carried. The ratio expressing increase in business can be clearly and accurately seen
from this method of portraying the facts
40
GRAPHIC METHODS
World's Work,
Fig. 42. Comparison of the Total Amount of Freight Service on the Railroads of
the United States in 1899 and in 1911
It would have improved this illustration if the two locomotives had been shown one exactly above the other
facing to the left. The additional cars representing the increase in 1911 would then be seen as though
added to the rear of the train
to be brought out is not that the railroads carried a larger passenger
in 1911, but that they carried more passengers.
If it is necessary to have a popular method, we can at least be
accurate by portraying the data in the form of Fig. 41, not as in Fig.
40. Copy for an illustration of this sort is very simply made by taking
proofs from a cut of one man and then pasting these proofs on a long
strip of paper until a row of the correct length is obtained. The whole
arrangement can then be photographed down to produce the effect
shown in Fig. 41. To avoid fractional men at the end of a row, it is
usually easy to express the ratio with a sufficient number of men in
each row or bar to get numerical correctness. Note that in Fig. 41
the whole arrangement is similar to that of Fig. 24 or Fig. 27 in Chapter
II, the actual data being given at the left of the row or bar. It would
have been better if the men in Fig. 41 had been faced to the left in-
stead of to the right. The additional men in the row for 1911 would
then appear to have joined the rear of the line rather than to have come
in at the front of the line.
1901
1912
World's Work
Fig. 43. Comparison in Size of Trainload on the Chicago, Burlington & Quincy Rail-
road hi 1901 and hi 1912
Here one locomotive is above the other but both face in the wrong direction. Figures for the data are not
given and the reader cannot tell whether the two lengths compared should include the locomotives or
only the cars. Clearness could have been assured if the cars had been shown for comparison in solid
black, with the locomotives included for pictorial effect, but only in outline
COMPARISONS INVOLVING- TIME
41
In Fig. 42 the idea is brought out that the railroads are now han-
dling more freight. The drawing, however, should be reversed so as to
have the two locomotives one above the other facing to the left, with
the additional cars at the right-hand end. It would also be better
if the dates for the two years and the figures representing tons had
been placed at the extreme left in the manner shown in Fig. 41.
In Fig. 43, the two locomotives are placed neck and neck, but
the whole chart reads backwards in that it reads to the left instead
of to the right. Turn the page over and hold it up to the light. Through
the back of the paper, the arrangement of the cars appears from left
to right as it should.
1870
1880
1890
I9OO
PRODUCTION
EXPORT
UPPER FIGURES
MILLIONS OF BALES
LOWER FIGURES
MILLIONS OF DOLLARS
Fig. 44. Yearly Cotton Production and Export of the United States. The Figures
with the Arrows Show the Number of Millions of Bales and also the Value in
Millions of Dollars
If horizontal bars are used to represent years, the earliest year should be shown at the top as seen here
No data are given in Fig. 43, and it is impossible to tell whether
the comparison' between 1901 and 1912 should be based on the ratios
of the whole length, including engines, or whether it should be based
on the lengths for cars only. A ratio without the engines would be
much larger than with engines. This chart is accordingly unreliable.
The difficulty in regard to engines being included in the drawing
could be entirely overcome if the freight cars were made in solid black,
with the engines shown in outline only, so that the eye could judge
the ratio between the solid black bars representing freight cars without
including the outline drawings of the engines.
Often in charting information like that given in Fig. 44, vertical
bars instead of horizontal bars are used. However, the figures given
in Fig. 44 in conjunction with the bars make it desirable that the bars
should here be horizontal in order that the figures may be read easily.
GRAPHIC METHODS
$990
AVERAGE VALUE OF AMERICAN AUTO EXPORTS
1912 Q
Ian r $1.100
1910| $1,380
1909 1 $1.700
1908 F
$1,880
The arrangement of dimension
marks with an arrow-head at each
end is a convenient scheme worthy
of wide use. Note that the per-
centage figures in the illustration
clearly refer to the value of the
cotton rather than to the number
of bales. The figures representing
time, in this case years, read down-
ward as they should do in every
case in which horizontal bars are
used to represent facts at different
periods of time. If the horizontal
bars are arranged with the earliest
date at the top, any reader who
wishes to do so may read the chart
as a curve from the left-hand edge
THE RISE OF THE LOW-PRICED CAR
SHOWING HOW THE AVERAGE VALUE OF EXPORTED
AMERICAN AUTOMOBILES HAS DROPPED IN FIVE
YEARS
World's Wort
Fig. 45. The Illustration and the Titles
are Shown Above Exactly as Origi-
nally Printed
The reader is misled if he does not notice that the
earliest year has been shown at the bottom
instead of at the top. The wording of the two
titles, when taken in conjunction with the chart,
really adds to the general confusion
of the page and the dates will then appear in correct order from left
to right.
In Fig. 45 the latest date has been placed at the top of the chart.
This causes an impression absolutely the reverse of what it was in-
tended to bring out
by the drawing. Any
one glancing at this
chart is likely to
suppose that the
earlier year is indi-
cated at the top and
probably would not
notice that the
draftsman in this
case, for some unjus-
PASSENGER AND FREIGHT REVENUES
(Average for U. S.)
PER MILE OF ROAD
Average
Aver
Av
Ratio of
No. of
No. of
per
Receipts
Journey
.Saul
Expenses to
D»te
Net
Operating
Passengers
Carried
Tons
Carried
Passenger
per Mile,
per Ton
per Mile,
per
Passenger,
per Ton,
Miles,
Operating
Revenues,
Revenue
1 Mile
1 Mile
Cents
Cents
Mites
Per cent
1908*
$3171
130073
974654
1.937
.754
32.86
143.83
69.75
1907
36%
123259
1 052 119
2.014
.759
31.72
131.71
67.53
1906
3548
114529
982401
2.003
.748
31.54
132.33
66.08
1905
3189
109949
8613%
1.962
.766
32.21
130.60
66.78
1904
2998
104 198
829476
2.006
.780
30.64
133.23
67.79
1903
3133
103291
855 442
2 006
.763
30.10
132.80
66.16
1902
3048
99314
793351
1.986
.757
30.30
131.04
64.66
1901
2854
89721
760414
2.013
.750
28.58
135.03
64.86
1900
2729
83290
735352
2.003
.729
27.80
130.87
64.65
1899-
2435
77821
659565
1.978
724
27.89
131.04
65.24
1898
2325
72462
617 810
1.973
'753
26.70
132.09
65.58
Fig. 46.
Courtesy of "Data," Chicago
Average Railroad Revenues from Passengers and
from Freight in the United States
Here again the earliest year has been shown at the bottom instead of at
the top. In tabulations of this sort there is less danger of erroneous
reading if the earliest year is shown at the top. Years are usually
grouped in fives, including in one group years ending from one to
five inclusive, and in the next group years ending from six to ten
inclusive
tifiable reason, has
reversed the correct
arrangement.
In Fig. 46 also,
the latest year has been placed at the top of the column instead of at
the bottom of the column. Though some precedent could probably
be found for such an arrangement, the arrangement nevertheless seems
COMPARISONS INVOLVING TIME
43
VALUE, AMERICAN EXPORTS
1906| [ $4,409,136
1911 1 $21,636,661 |
1 91 2 1 $28,300,139
VALUE, IMPORTS FROM ABROAD
1906 1 |
1911
an unfortunate one which should
not be copied. Note that in Fig. 46
the figures have been arranged in
groups of four with a blank space
to assist the eye in reading across
the page. In general, it is cus-
tomary to have such figures not
in groups of four but in groups of
five, the groups including years
ending in 1 to 5 inclusive and 6 to
10 inclusive.
A rapid reader seeing Fig. 47 is
likely to get a much exaggerated
idea of the increase in the Amer-
ican exports of automobiles. The
arrangement of the three hori-
zontal bars for the three years is
such that the reader is justified in
assuming that the years are con-
secutive. He is not likely to
notice that the upper bar repre-
sents the year 1906 and that four
years are omitted between 1906 and the consecutive years 1911 and
1912. Since there is nothing to indicate that years have been left
out after 1906, the reader seeing
the figure 1912 is apt to assume
that the two earlier years are 1911
and 1910.
Fig. 48 is a redrawing of Fig.
47 with a change in scale to indi-
cate to the reader that the earlier
year shown for comparison must
not be read as one of three con-
secutive years. Though the space
left between the bars for 1906 and
$4,910,208
$2,446,248
$2,000,000
A MARVEL OF EXPORT TRADE
SHOWING THE AMAZING INCREASE IN OUR EXPORTS
OF MOTOR CARS, AND THE STEADY DECREASE IN OUR
IMPORTS, IN THE LAST SEVEN YEARS
World's Wort
Fig. 47. This Illustration was Originally
Printed with Fig. 45 on the Same
Page of a Magazine, yet in Fig. 45
the Earliest Year was Shown at the
Bottom While Here the Earliest Year
is Properly Shown at the Top
There is, however, danger, in this illustration, that
the reader may assume that the three bars rep-
resent consecutive years without noticing the
jump from 1906 to 1911. Compare Fig. 48
VALUE, AMERICAN EXPORTS
1906 * 4, 409,1 36 ••
1911
1912
21,636,661
28.3OO.139
VALUE, IMPORTS FROM ABROAD
1906
1911
1912
4,910,208
2,446,248
2,000,000
Fig. 48. The Contrast of American Ex-
ports and Imports of Automobiles
The data of Fig. 47 have here been redrawn. The
values have been shown at the left of the bars,
where they give the neatest and most convenient
arrangement. Note that the bar for 1906 is
somewhat separated from the bar for 1911, so
as to indicate to the reader that the three bars
do not represent consecutive years
1911 would not be sufficient for
the four omitted years, if the
whole chart were drawn to scale,
the space is nevertheless large
44
GRAPHIC METHODS
enough to serve as a safeguard to the reader. A slight break could
indicate in this manner a gap of any large number of years which it
would not be feasible to denote by allowing space according to scale.
In Fig. 48 the years and the figures for the chart are properly shown
to the left much as they are shown in Fig. 24 and in Fig. 27.
1912
191!
1911
BU.
BU.
19U 1912 1911 1912
New York Times Annalist
Fig. 49. The Size and the Value of the Corn Crop of the United States in 1911 Com-
pared with that of 1912
The object of the chart is to show that, though there were more bushels of corn in 1912, the producer re-
ceived less total money than in 1911.
The left-hand illustration is incorrectly made as it shows the earlier year to the right. In the central
illustration this error has been corrected and the years are named at the base instead of at the top.
The arrangement still fails, however, to bring out the message clearly.
From the right-hand presentation it can be seen instantly that the number of bushels has increased while
the total money received has actually decreased. The right-hand presentation is arranged in accord-
ance with the working of the average person's mind and it gains in clearness accordingly
The left-hand group in Fig. 49 was used as an illustration in a
business magazine. The purpose of the chart was to show that in
1912 the farmers of the country raised more bushels of corn than in
1911 but received less total money in return. Note that the earlier
year is placed at the right instead of at the left, and that the dates
•are given at the top rather than at the bottom. The middle group
of bars corrects the error, but the information is still not as clearly
brought out as it should be. The best way to bring out this informa-
tion is to show that the number of bushels has increased while the
number of dollars has decreased, and this is not clear from the middle
drawing. In the right-hand presentation it is clearly seen that the
bushels went up though the total value came down. The right-hand
drawing follows the working of the average person's mind and it gains
in clearness accordingly.
As a general rule dates should always be arranged to read from
left to right, and columns of figures should be arranged with the col-
umn for the earlier date at the left. A common exception is made,
however, in the case of financial reports when it is desired to show
the most recent year next to the various type-headings relating to
COMPARISONS INVOLVING TIME 45
earnings, expenses, etc., as in Fig. 50. In the case of financial reports
it is always the latest year which is of chief interest, and for this reason
the arrangement of Fig. 50 seems permissible in order that the figures
and the account names may be side by side. The problem in Fig. 49
is so entirely different from that in Fig. 50, that the method of Fig. 50
cannot be held as a precedent to justify the reversed arrangement
of dates shown at the left of Fig. 49. The fact that one needs an
umbrella on a rainy day is not sufficient reason for carrying an um-
brella at all times.
* * *
UNION BAG AND PAPER COMPANY— Reports for
the year ended Jan. 31:
1913. 1912. 1911. 1910.
Net earnings $554,251 $1,017,835 $1,038,112 $1,055,400
Depr. and ext. fd. 122,585 122,2(55 120,987 149,925
Balance 431,666 895,570 917,125 905,475
Skg. fd. & bd. red. 134,025 114,095 110,745 107,603
Balance 296,741 781,475 806,380 797,870
Interest 253,748 202,480 197,135 204,611
Balance for divs.. 42,993 578,995 009,245 593,259
Preferred dividend 330,000 440,000 440,000 440,000
Deficit 287,007 *138,995 *169,245 "153,259
Prev. surp 1,921,788 2,020,471 1,851,226 1,697,968
Bond disc. & exp. 70,945 237,677
Profit and loss sur.1,563,836 1,921,788 2,020,471 1,851,220
# • •
New York Times Annalist
Fig. 50. Brief Financial Statement Regarding the
Union Bag and Paper Company
In condensed statements of this sort there seems to be good
reason for placing next to the headings at the left the column
of figures for the latest fiscal year, since this information
is of most vital interest to the reader. Columns -for other
years are then printed to the right for comparative pur-
poses. The earliest year is shown at the extreme right
Though this reversed arrangement of years seems permissible
for the purpose of printed reports as here used, there is
no justification for the use of the reversed arrangement in
chart work. As a general rule material given by years
should be shown with the earliest year at the left
Fig. 51 is an illustration photographed down from a large drawing
used in a wall exhibit. It is a fair example showing what can be done
to arouse interest by the judicious embellishment of charts, especially
of those for wall exhibits intended to reach a miscellaneous audience
having an average of rather limited education. Note the smoke-
stacks in Fig. 51. The smoke-stack at the left is the same height as
the bar for the year 1906-07, and the taller smoke-stack at the right
the same height as the bar for 1912-13. As this drawing was made
for a wall exhibit to show the co-operation of manufacturing companies
with the college, the pictorial embellishment seems quite justifiable
and useful to attract attention to this particular exhibit. A pictorial
46
GRAPHIC METHODS
CO-OPERATING WITH THE
-• ENGINEERING COLLEGE
OF THE
UNIVERSITY OF CINCINNATI
HAS INCREASED 288
II
III
_^
effect also relieves monotony in a large exhibition which may have
hundreds or even thousands of different charts and other wall exhibits.
Fig. 52 was shown in conjunction with Fig. 51 with the idea of
pointing out that the number of students in the University of Cin-
cinnati had increased just as (according to Fig. 51) the number of
firms co-operating in the engineering work of the University had
increased in the same time.
The bars in Fig. 51 and
Fig. 52 are placed vertically,
each bar representing a year.
This vertical arrangement of
bars permits reading the chart
as if a curve had been made
by drawing a line through the
tops of all the bars. Curves
are the common language of
engineers and statisticians.
In order that the bars may
be read as curves, it is desir-
able to have the bars placed
in a vertical position, if they
represent divisions of time,
rather than entirely distinct
subjects such as the separate
cities compared as to the
value of their output of manu-
factured products, in the chart
reproduced in Fig. 21.
Lettering like that shown in Fig. 51 or Fig. 52 is conveniently
made by using the gummed black-paper letters and figures which can
be obtained in many good stationery stores. A thin pencil line as a
guide at the bottom of the letters, and some judgment used in spacing,
will assist greatly in getting a neat result from the gummed letters.
Large bars like those shown in Fig. 51 and Fig. 52 can be made by
cutting out strips of black paper and pasting them onto white card-
board. Such work, however, must be very carefully done or the bars
will curl on the edges and give an unpleasant effect. It is generally
better to use India ink in making the bars if a good result is to be
assured. The liquid drawing ink sold at most stationery stores is
Fig. 51. The Increasing Number of Business
Firms Co-operating with the Engineering
College of the University of Cincinnati
When the bars represent years or other divisions of time,
a vertical arrangement of the bars is usually more
desirable than the horizontal arrangement seen in Fig.
44. With the vertical arrangement a line may be
imagined joining the tops of the bars so as to give a
"curve".
Note, in this illustration of a wall chart, the popular touch
given by the pictures of manufacturing plants with
smoke-stacks of the same height as the first and the
last vertical bars
COMPARISONS INVOLVING TIME
47
INCREASE IN STUDENTS
CO-OPERATIVE COURSE
ENGINEERING COLLEGE
INCREASE 1913 OVER 1907
1252
84
ill
available in many different colors. Some grades of the drawing ink
are water-proof after drying. On elaborate charts the water-proof
quality should always be used to make certain that a few rain drops,
or handling with moist hands, will not ruin the finished work.
In the discussion of Fig. 51 and Fig. 52 it was mentioned that a
line could be drawn through the tops of the vertical bars to give a
curve. If the curve were actually drawn, the bars themselves would
be omitted. In Fig. 53, instead of using bars,
we have lines which may be considered as curves
for each of the several items compared. In this
case it would be impossible to use bars for each
of the items shown because the bars would cover
each other. The bars are entirely omitted and
lines are simply drawn from the 100 per cent
point in 1897 to the various points for different
items in 1907. It is certain that the prices (that
of pine lumber, for instance, shown by the upper
curve) did not have the uniform rate of increase
which the straight line from 1897 to 1907 would
indicate. We are considering here, however, the
changes over the period as a whole, and we can
for simplicity draw a straight line and neglect
all the fluctuations of intervening years. The
general scheme of Fig. 53 is convenient, as the
neglect of detail brings the main information out
clearly. Fig. 53 has, unfortunately, been drawn
in a misleading manner in that the reader is
likely to interpret the curves as if zero were
shown at the bottom of the chart. The general
rule in charts of this kind is that zero should be
shown as the bottom line, or, if not shown at the
bottom, that the omission of zero should be
clearly indicated. As Fig. 53 is shown on a per-
centage basis, the 100 per cent line should be
clearly indicated by drawing a broad line on the
chart for the line opposite the figure 100 in the
scale. It would have been better, perhaps, to have plotted the data
so that zero would replace the figure 100. On a scale so made, pine
lumber would go up 83 per cent, while railroad rates would be shown
American Review of Reviews
Fig. 52. The Increasing
Number of Students in
the Co-operative
Course of the En-
gineering College of
the University of Cin-
cinnati
This illustration was originally
used as a companion piece
to the chart of Fig. 51. For
a popular exhibit the use of
vertical bars brings out in-
formation quite clearly.
Though curves (such as are
shown in later chapters) are
superior to vertical bars, it
is unfortunately true that
most people do not know
how to read even the sim-
plest curves correctly.
Note the lettering at the upper
portion of the chart. Letter-
ing of this kind may be had
by using separate gummed
letters such as may be pur-
chased ready for use
48
GRAPHIC METHODS
1897
1907
as decreasing 4 per cent. The scale would read upward from the
zero line for increases, and downward from the zero line for decreases.
By changing the scale and using a broad zero line, misinterpretation
of the chart would be entirely prevented.
Fig. 54 is somewhat similar to Fig. 53 in that intervening years
are neglected, and that lines drawn from left to right of the chart
indicate the total movement rather than short-time fluctuations.
Fig. 54 would be better if the lines around the outside of the drawing
had been omitted. In general, lines of this kind around the outside
of a chart are likely to be confusing. In this case, the double lines
at the bottom of the chart draw too much attention to the bottom
and may cause a wrong interpre-
tation of the chart. As charts of
this type are usually made so as
to have the bottom at zero, the
reader of Fig. 54 may get an en-
tirely erroneous idea of the actual
increase in the rates of wages. This
chart of Fig. 54 should have been
drawn with J/g inch more room at
the bottom so that the scale would
begin at zero rather than at $1.00.
A glance at the chart as it is shown
here might convey to any but a
careful reader that the wages of
trackmen had more than doubled,
within the period of ten years
covered by the records thus graph-
ically presented, though the ac-
tual wage increase was only from
about $1.12 to $1.50. Though Fig.
54 contains a good suggestion for
presenting data in popular form,
it is in itself misleading because it
does not have its base line at zero.
Fig. 55 is a commendable piece of work for popular presentation,
as for instance in a magazine. Note the use of dimension marks in
two independent horizontal rows so that the upper row indicates the
material from which the ships are made while the lower row shows the
$100
Reproduced by Permission from Droege's "Freight Terminals and
Trains", copyright, 1912, by the McGraw-Hill Book
Company
Fig. 53. Changes after Ten Years in Costs
of Railroad Materials and in Freight
Rates for a Large Railroad System
A simple chart of this kind is often advantageous,
as it neglects all temporary fluctuations and
shows only the important changes over a period
of time considered as a whole. The line for 100
on the scale should have been made a broad line
to indicate the basis of comparison. A wavy
line should have been put at the bottom of the
chart to show that the scale does not begin at zero
COMPARISONS INVOLVING TIME
49
method of propulsion. Dimension lines used in this way are an ex-
tremely valuable adjunct to chart work and should be used much more
commonly than they are at present.
Tendencies for the future are
frequently very accurately pre-
dicted by drawing a smooth curve
through known points and then
continuing this curve for future
years in the manner shown by the
broad line in Fig. 55. The trend
of this curve indicates that by
1925, we are likely to have ships
about 1,200 feet long. Though
the method of prediction by ex-
tending a curve into the future is
very valuable, care must always be
used to apply the method with
judgment. If in Fig. 55 a curve
had been drawn from the data up
to the year 1860 and extended
from that point to show the prob-
able length of vessels in succeeding
years, the curve would have indi-
cated a likelihood of 1,200-foot
ships by 1870. We can see in the
light of history that such a predic-
tion would have been most errone-
ous. It would have assumed the
continuance of side-wheel steamers
and would have been based chiefly
on the length of the Great East-
ern alone. The Great Eastern
was too far in advance of the age and was in reality an engineering
failure. Hence, we see the error which would result from basing a
prediction curve on too limited an amount of data.
Periodic photographs of any kind of construction work are one
of the most striking forms of graphic presentation. Many large
contractors and machine manufacturers now make a practice of
having photographs taken of each job at least once each week. The
THE RISING WAGE SCALE
SHOWING THAT THE PAY OF RAILROAD EMPLOYEES
HAS INCREASED FROM 30 TO 50 PER CENT. IN TWELVE
YEARS. NOTE THAT THE GENERAL OFFICE CLERKS
NOW RECEIVE LESS THAN THE TRAINMEN.
World's Wort
Fig- 54- Wage-Scale Increase
This illustration is so drawn that wages appear to
have increased much more rapidly than is
proved by the actual data given in the chart it-
self. The chart should have been extended to
show the zero line of the vertical scale so as to
assist the reader in getting a correct interpre-
tation
50 GRAPHIC METHODS
photographs are carefully dated and filed for reference in case there
should be any dispute later regarding the progress of the work and
payment therefor. If a large card giving the date of the work is placed
in front of the camera so that the date is photographed directly into
the picture, the date is somewhat more easily proved than it would
be otherwise. Putting the date card in front of the camera with the
date upon the card gives a chance for any passer-by to check the hon-
esty of the date on the picture, much as the "amount purchased"
card at the front of a cash register checks the honesty of the clerk.
Progress photographs like those described above are particularly
effective for use in advertising. A series of three or four pictures
placed one below another, with the dates carefully stated on each,
give the best possible demonstration of the rapidity with which con-
struction work has been completed by the advertiser. A broad use
for these progress photographs is found in the preparation of reports,
catalogues, magazine advertising, etc. Thus a manufacturing plant,
for instance, can be pictured in a series of photographs taken some
years apart showing buildings which have been added to provide for
increase in the business. In the case of machinery, a series of photo-
graphs taken in different years are of value to show the increase in
the size of the machines built or the successive improvements made
in the design.
Moving-picture machines have opened up a whole field of possi-
bilities in the rapid conveying of accurate information. Many com-
panies are now using moving-picture films to show the technical
operations involved in making up their manufactured product, or to
show views in different parts of a factory. Moving-picture cameras
have been used, also in a very striking way by Mr. Frank B. Gilbreth
as an adjunct to methods of time and motion study. By placing in
the camera field with the worker a clock with a large dial and a sweep-
ing second hand, an automatic and permanent record may be secured
both of the worker's movements and the corresponding elapsed time.
The statistics thus graphically recorded are immeasurably more
accurate and more conclusive than any that could be secured in any
other way. Possibilities for the use of moving-picture machines in
educational work in schools are only beginning to be grasped by a
few of the world leaders in thought. When the moving-picture ma-
chine becomes a feature of every school room the results will be as-
tounding.
COMPARISONS INVOLVING TIME
1840 1950 1860 1870 1880 1890 1900 1910 1913
}< WOOD
PADDLE WHEELS
1 SCREW f— 2 SCREWS *-4 SCREWS TURBINES-J
Fig- 55- The Growth in the Length of Ocean Liners
World's Work
This is an excellent piece of presentation for reaching an average non- technical class of readers. A smooth
curve line has been drawn through the ends of the pictured ships so as to approximate most closely the
general law which seems to govern progress in ship building. The smooth curve has been extended into
the future as a prediction of the length of the ships which will probably be built during the next ten years.
Note the excellent use of dimension-line arrows at the base of the chart showing the materials used in ship
building and the methods of driving ships at different periods in history
Bars to represent different intervals of time as in Fig. 51 and
Fig. 52 may be compared to the progress photographs mentioned
above. Though the bars and progress photographs are valuable,
they may be said to give information only in spots. A moving-picture
machine shows pictures so rapidly that the pictures blend into a con-
tinuous narrative in the eye and the brain of the observer. What the
moving picture is to separate progress photographs, the curve is to
detached bars representing time. In just so much as the moving
picture is superior to separate pictures shown by lantern slides, in
just that much is a curve superior to a series of horizontal or vertical
bars for the same data. Unless a person knows thoroughly how to
read and how to plot curves he cannot hope to understand the graphic
presentation of facts. The use of curves will be covered in later chap-
ters.
CHAPTER IV
TIME CHARTS
THE horizontal-bar method used in Chapter I to show the com-
ponent parts of any unit may be modified so as to represent
various conditions at different hours, days, and other sub-
divisions of time. Fig. 57 illustrates a convenient scheme to assist
the arrangement of vacations for concerns having many employees, in
which it is necessary to plan the vacations so that there shall always
VACATIONS FOR THE YEAR 1912
16 22 29
Sept.
Fig. 57. Chart for Assigning Vacation Periods in a Large Office
Vacations have here been phoned so that not more than two men are away at any one time
53
54
September-^
GRAPHIC METHODS
October- ->)< November
_S3aS_S^Q
\Bonus Earn eat, is Bonus Lost oc Day Work t3 Day Absent. Heavy vertical lines indicate Sundays.
CD |6
*!f
e!4
o!2
Fig
The
V
zrs
Jlfr. /f. i. Gantt, in Journal Am. Soc. Mechanical Engineers
, 58. Chart Illustrating Bonus Work in a Factory where Bonus Work was Intro-
duced Too Rapidly at First
curve at the bottom shows the total number of workers earning a bonus each day. On November 22
all the workers earned a bonus
be a good man available to take charge of responsible work. A chart
of this kind can be made quickly if co-ordinate paper is used, the hori-
zontal lines being drawn in with lead pencil. Vacations are shifted
around until an arrangement is found that is satisfactory to the man-
ager and also to the various employees. After a final schedule has
been decided upon, the time given each employee can be made suffi-
ciently conspicuous by going over the lead-pencil marks with crayon
or ink. A chart of this nature posted on the bulletin board of an
office would serve as a convenient means of giving information to
the employees as to their respective vacation periods.
Fig. 56 (page 52) illustrates a method regularly used by Mr. H. L.
Gantt to indicate conditions in a manufacturing plant. This particular
chart was drawn to show progress made in training the employees
of a worsted mill under scientific management. Trained employees
TIME CHARTS 55
may earn a bonus by completing a certain quantity of work each
day. It will be seen at a glance that the chart becomes blacker at the
right hand, thus showing that two-months training had greatly in-
creased the output of the employees. If a chart like this is made
with different colored pencils, the facts can be grasped more quickly
than when only one color is used.
Fig. 58, at the right-hand end, shows that the workers were earning
a bonus practically every day, and it also shows clearly that some-
thing was wrong during the middle part of October. The workers
failed to earn a bonus at that time for the reason that the bonus work
was introduced so rapidly that they did not get adequate instruction.
The manager of a plant would realize such a situation at once if he
had this kind of a chart before him.
At the bottom of Fig. 58 a curve is plotted to give the number
of operators who earned a bonus every day. The horizontal scale for
this curve is exactly the same as for the bar chart above, except that
in the curve a day is represented by a line rather than by a space.
In plotting curves, it is customary to represent time by lines rather
than by spaces, and this curve is plotted in accordance with good
practice. The scale at the left-hand edge of the lower part of the
chart represents the number of workers who made the bonus. In
order to plot the curve, one simply counts in the upper section of the
chart the number of black blocks which are filled in for the particular
day. Thus, for October 10, we see that there are seven black blocks.
The point on the curve is then placed in the lower portion of the chart
at the intersection of the horizontal line representing the number
of workers earning a bonus and of the vertical line representing the
day, October 10. The curve gives a convenient method of deter-
mining the total number of operators who are earning a bonus. When
it is desired to know only the number of employees earning bonus
each day, the curve shows the matter more clearly than do the black
blocks in the upper portion of the chart. The horizontal bars give
the story for each worker, the curve gives the total for all the workers.
1 A chart like that shown in Fig. 59 would ordinarily be made on
a long sheet of co-ordinate paper so that the co-ordinate ruling could
be used for the vertical lines, indicating time. Co-ordinate paper in
several different rulings can be purchased in rolls so that the desired
ruling can often be had in continuous lengths. Sometimes, however,
the desired ruling can be obtained only in flat sheets of limited size
56
GRAPHIC METHODS
TIME CHARTS 57
and it is then necessary to make a long sheet by pasting together
several of the separate sheets. The original study from which Fig. 59
was prepared was made upon a built-up sheet seventeen inches wide
and eight feet long, so that a full month of lighter operation could be
shown on the one chart.
In a large working chart, such as is shown in Fig. 59, very little
ruling is required except for the lines limiting the width of the hori-
zontal bar representing each lighter. In the original chart, drawing
inks of different colors were used to indicate the four different condi-
tions— working north and working south, and idle north and idle
south. Black was used to indicate towing. Solid red showed idle
time in the north, and a red made up of red-ink strokes with white
spaces showed idle time in the south. Thus all idle time may be
indicated by red, the method of application determining whether the
delay is at the north or at the south end of the trip. Working time
may similarly be indicated by solid green and by green strokes with
white spaces.
It is desirable in all chart work to have certain conventions by
which colors would be understood to have certain definite meanings.
Thus, following railroad practice, red could generally be used in chart
work to indicate dangerous or unfavorable conditions, and green to
indicate commended features or favorable conditions. Where neither
commendation nor adverse criticism is intended, colors such as blue,
yellow, brown, etc., could be used.
In Fig. 59, an ordinary atomizer filled with writing ink was used
to fill in gray areas representing night hours. If a little care is used
in regulating the spray, a good uniform and light shade of gray is
obtained, on top of which colored crayons will show out clearly, as,
for instance, in Fig. 59 where Lighter No. 7 is represented as working
on the night of September 23. To prevent the ink spreading over
the chart, a strip of cardboard should be laid carefully on each edge
of the surface which it is desired to ink in by means of the spray.
In making up charts like that shown in Fig. 59, the data are usu-
ally recorded on the chart day by day as reports come in. This in-
volves a large amount of handling of the chart, and the chart is likely
to be much smeared by the time the last reports are entered. If col-
ored crayons with the color embodied in paraffin are used, very brilliant
colors can be obtained, yet rubbing with the hands will not smear
the colored areas. Unless a non-smearing crayon is used, it is better
58
GRAPHIC METHODS
Fig. 60. Operations of Three Tug-boats in New York for Twenty-four Hours. The
Boat Represented by the Lower Bar is in Service for a Twelve-Hour Shift Only
A working chart of this kind would usually be made on a long strip of co-ordinate paper. The illustration
was drawn entirely by hand to show the possibilities of hand cross-hatching for bringing out information
ordinarily shown in several colors
to make up colored charts by using different colors of drawing ink.
The ordinary crayons smear so badly that a chart made with them
is sometimes unrecognizable before it is finished.
Fig. 60 is a further elaboration of the method used in Fig. 59.
The actual chart from which this illustration was made was drawn
on co-ordinate paper ruled in tenths of an inch. Each of these tenth-
of-an-inch spaces was made to represent ten-minutes time, so that a
much larger scale wras obtained than in Fig. 60. As the tug-boat
captains regularly kept log-books in which their work was recorded
to a five-minute interval the chart was made to the same interval
by splitting the ten-minute squares to represent five-minute intervals.
With a scale of this size it was feasible to use colored crayons, even
though some of the divisions of time were very short.
Fig. 60 was drawn by hand and shows the possibilities in preparing
an illustration of this kind when only one color of printing ink is
available.
The chart from which Fig. 60 is taken was made to determine how
much idle time there was in the operation of three tug-boats, and to
ascertain whether the boats could be so run as to reduce the amount
of idle time and give better service. The black in Fig. 60 shows the
idle time vividly. By looking from bar to bar, it is possible to study
all the work of the three tug-boats and to determine whether, if the
work were differently assigned, there would be less waiting between
jobs. Frequently the tug-boats had to tow two or more lighters or
two or more car-floats, simultaneously, as will be seen from the extra
TIME CHARTS 59
bars placed below the main bar for each tug. The number of lighters
and car-floats towed simultaneously is clearly shown in the chart, as
well as the time at which each was picked up, and the time at which
each was delivered by the tug. In the case of car-floats, a frequent
break will be noticed at the end of the towing, one-half the width of
the horizontal bar being marked with black. This convention was
adopted to show that the idle time was occasioned by the necessity
of waiting to obtain an unoccupied float bridge into which the car-
float could be shifted. Though the tug-boat was standing idle it was
not feasible for the dispatcher to take the tug away from the par-
ticular car-float to which it was attached, for the tug would be neces-
sary to place the car-float in the float bridge as soon as the float bridge
became .free.
Charting of information frequently brings out points which would
be entirely overlooked if charts were not made. The tug-boat chart
from which Fig. 60 was taken at once calls attention to the time re-
quired for the tugs to obtain water. As the service of tugs was valued
at about $9.00 per hour, the time spent in taking water was a serious
loss. As soon as the chart showed the extent of this loss, it was com-
paratively simple to remedy the situation by providing different
methods of getting boiler-feed water.
A time chart like Fig. 60 can often be used advantageously in
conjunction with other time charts covering the same period of time.
Thus, in studying tug-boats, the information on a chart for lighter
operation such as is shown in Fig. 59, and on charts for the operation
of car-floats or of float bridges, may be valuable. All the various
kinds of equipment with which the tug-boats may be employed could
be considered in the study, if it is to be determined whether or not
the most effective use is being made of the tug-boats. If all the charts
used in the study are drawn to the same horizontal scale, the charts
can be placed immediately above each other so that the operations
of all related equipment for every hour of the day and night can be
instantly seen during the whole of a test period, of, say, a week or a
month.
The charts thus far considered in this chapter have shown time
in the horizontal direction only. In Fig. 61 we have time shown by
days in the horizontal direction and by hours in the vertical direction.
This type of chart is extremely valuable in determining whether or
not schedules are maintained uniformly over any period of time.
60 GRAPHIC METHODS
By using different colors of ink a chart of this kind can be made so
as to show all related operations without the drawing becoming too
complex to read. Fig. 61 has purposely been made simpler than the
ordinary chart of this kind to overcome the handicap of being limited
to only one color of ink in the reproduction.
Charts in the form of Fig. 61 are valuable in that they show on
one sheet all the operations occurring during a given period of time —
in this case, twenty -four hours. Some conditions, such as the blizzard
of January 7, affect all the deliveries to the different railroads. Study
of the chart brings out in contrast conditions which are beyond the
control of man and conditions which are the result of carelessness
or poor management, which usually crop up first in connection with
one railroad, then in connection with another, without being so gen-
eral as to affect all of the curves, as did the blizzard of January 7.
Fig. 62 shows the possibility of simplification when so many dif-
ferent horizontal curves must be shown that easy reading is impossible.
The simplification is made in Fig. 62 by showing only one railroad
on each sheet. All the figures for one railroad are shown in curves,
placed one above the other. Ordinarily curves like those in Fig. 62
will be nearly parallel, for the time interval required to complete
each of the steps of work remains about the same day after day. What
Fig. 62 brings out most of all is not so much the time interval between
the different steps as the information as to whether each of the dif-
ferent steps was started promptly on schedule. Any one operation
started late must delay all the following operations.
The paper on which Fig. 62 was drawn is in itself worthy of at-
tention. This letter-sheet size of paper was carefully laid out so that
a typewriter could be used for the lettering on the margins of the four
sides of the sheet. The paper was purposely ruled in squares so that
any of the common divisions of time might be shown. The possibilities
in this direction are:
The days of the month may be used on the short edge of the paper
as in Fig. 62.
Fifty -two weeks for one year can be shown by using the long edge
of the paper.
Three years by months can be plotted by using the thirty-six
squares on the short side of the paper.
One year by months can be shown by using every third line along
the short edge of the paper.
TIME CHARTS
61
1AM
12
II P.M.
10
9
1 P.M.
12 M
HAM
1O
9
8
7
\
\ \
«n. 1 2 3 4 5 6 7 8 9 1O 11 IE 13
NewYears Sunday (Blizzard) Sunday
is
Fig. 61 . Operation of Freight Car-Floats at a Railroad and Steamship Freight Terminal
Here we have time represented by days in the horizontal direction and by hours in the vertical direction.
The object of the chart is to record whether car-floats are loaded and dispatched at the same hour each
day.
Dotted lines show the time at which cars are pushed onto car-floats by locomotives. Solid lines show
the time at which car-floats are towed away by tug-boats. Curves for any one car-float destination are
in pairs bearing the same letter.
If the departure schedule is well maintained, all curve lines will be practically horizontal. Note that the
blizzard of January 7 affected the locomotives less than the tug-boats
GRAPHIC METHODS
ARRIVAL AffD BRIDGETS TIME
Of
X Y 2 EAUHOAD GARPLOAT FOR MAY.
c
Sunday.
A
Arrived - tine D ---- Bridged - time
„ E - Waiting for bridge - hotirs,
- Loaded - time ~R . Departure - time.
Fig. 62. Operation of Freight Car-Floats at a Railroad and Steamship Terminal
In Fig. 61 several different railroad connections were shown on one large sheet. Here, in Fig. 62, but one
railroad is represented on one sheet, with the idea of using as many sheets as there are railroad connec-
tions.
This illustration is photographed down from a sheet of 8j^-inch by 11-inch co-ordinate paper specially
designed for use with a typewriter. The zinc cut for this illustration was made directly from the type-
written original
TIME CHARTS 63
Percentages up to 100 per cent can be indicated by using fifty
of the fifty-two squares on the long dimension of the paper. This
ruling gives a co-ordinate paper which is extremely convenient for
general work. Other charts drawn on this same ruling of paper may
be seen in Figs. 134, 130, 103, 156.
Fig. 63 was adapted from a chart shown in the United States
Statistical Atlas for the Census of 1900. The Atlas illustration was
printed in color, while Fig. 63 is in black ink. The scheme of this
chart is one which could be used widely, for it is an extremely con-
venient method of showing a frequently changing rank for a large
number of units. The blocks for the various States are numbered
according to the rank of each State at the first year shown at the left.
The rise or fall in rank of each State at each census can be seen at once
by following the lines joining the numbered blocks. The actual nu-
merical rank at each census is seen by reading horizontally to the rank
number at the right-hand margin or to the numbers in the left-hand
column of blocks.
Sales managers publishing a house organ may find the method
of Fig. 63 of great advantage in showing the status of each branch
selling-house or the rank of each salesman. If every member of the
selling organization is given a confidential number, the rank of each
can be shown in the house organ sent out each month. Branch houses
can be encouraged to compete with each other if their relative rank
month after month is indicated on the chart. In the case of salesmen,
if the numbers are kept confidential no one salesman can tell from the
chart anything about any other salesman. He could, however, see
very clearly that his own position in the sales force was getting better
or worse, according to whether his relative-rank line pointed upward
or downward. This comparison of selling units on a rank basis is in
many respects fairer than any curve based on the value of sales. Good
business conditions or bad business conditions affecting all alike do
not show up in charts like Fig. 63. What is shown is the real progress
or lack of progress made by every man or branch selling house as
compared with all the others.
Printer's copy for a chart like Fig. 63 can very easily be made
up if printed strips of the blocks shown in the chart are used. These,
if desired, could be made from Fig. 63 itself. Simply photograph
the chart, then take one vertical row of the blocks, as for the year
1900, and have a line engraving made of them, eliminating the figures
64 GRAPHIC METHODS
for numbers which appear in the middle of each block. Print from
the zinc plate a number of strips of blocks. With shears and a paste-
pot, another vertical row of blocks may be added at the right-hand
edge of the chart copy each month to provide "copy" for the plate
to print the succeeding month's illustration. The identification could
be lettered by hand inside of the vertical row of blocks for the latest
month. It then takes only a short time to draw lines joining blocks
having corresponding numbers. The built-up "copy" is then ready
for the engraver to make a zinc plate. Zinc plates cost so little that
there is almost negligible expense required for the new line cut needed
each month.
In Fig. 64 the general scheme of Fig. 63 is expanded so that the
chart shows not only the rank, but also the comparative size of the
units under consideration. This illustration shows also some inter-
esting combinations of shading by means of which blocks of distinctly
different appearance are obtained. Fig. 64 was photographed directly
from a United States Government report. Otherwise, the years
would not be shown here reading from right to left instead of from
left to right. Though the right-to-left arrangement is unfortunate,
the general scheme of Fig. 64 is excellent, as it gives a large amount
of information in a small space. The convenience due to this method
of double comparisons, either horizontal or vertical, gives it a decided
advantage in clearness.
Train charts like that shown in Fig. 65 are very commonly used
by railroads, rapid-transit subways, etc. Fig. 65 would not look so
complex if colored ink were available to show in contrast the express
passenger trains, the work trains, etc. It is suggested that the reader
observe the key at the top of Fig. 65 and then follow a few of the
various trains from one end of the line to the other, taking into con-
sideration the fact that this is a single-track railroad and that trains
must pass at the turnouts which are available. To schedule a pas-
senger train such as that leaving Tyrone at 12:25 p. m. is no simple
proposition on such a crowded railroad as this.
In rapid-transit work in large cities a time-distance chart in the
general scheme of Fig. 65 is almost essential if methods of giving
high-speed service to the people are to be studied. These time-distance
charts can be made on so large a scale that two horizontal lines may
be used to indicate the stations, with the lines spaced a distance apart
to show to scale the actual length of each station platform. Time-
TIME CHARTS
65
I860
1870
1880
1890
1900
Montana.
Idaho
Dakota
Arizona.
Wyoming
RanK
1 New York
2 Penn.
3 Illinois
4 Ohio
5 Missouri
6 Texas
7 Mass.
8 Indiana
9 Michigan
10 Iowa
11 Georgia
12 Kentucky
13 Wisconsin
14 Tennessee
15 N.Carolina
16 New Jersey
17 Virginia
18 Alabama
'9 Minnesota
20 Mississippi
21 California
22 Kansas
23 Louisiana
24*8. Carolina
25 Arkansas
26 Maryland
27 Nebraska
28 W. Virginia
29 Connecticut
30 Maine
31 Colorado
32 Florida
33 Washington
34 Rhode Isl'nd
35 Oregon
36N.Hampsh'e
378. Dakota
38 Oklahoma
39 Indian Ter.
40 Vermont
41 N. Dakota
42 Dist. of C.
43 Utah
44 Montana
45 N. Mexico
46 Delaware
47 Idaho
48 Hawaii
49 Arizona
SOWyoming
51 Alaska
52 Nevada
Adapted from the United States Statistical Atlas
Fig. 63.
Rank of States and Territories in Population at Different Census Years
from 1860 to 1900
Each State is represented by a block bearing an identifying number. The change in rank from census to
census is indicated by the connecting lines. Actual rank at any census can be seen by referring horizon-
tally to the figures at the right or to the figures at the left.
A. chart of this kind can be used for showing relative rank of salesmen or comparative sales of different
branch sales-houses *
66
GRAPHIC METHODS
°^^ fl
M «*- -g
<a y a
S B.2
*j •*• *j
,5 I
TIME CHARTS
6?
68 GRAPHIC METHODS
distance curves like those shown in Fig. 65 are then plotted, one for
the rear end and another for the front end of each train. As the train
remains constant in length throughout one whole journey it is obvious
that the two curve lines must be a constant vertical distance apart
throughout the length of the chart. At stations, subway trains must
stop in such a way that the whole length of the train will be opposite
the platform so that passengers may get in and out of every car. The
trains follow each other very rapidly, and it is essential that sufficient
room be left between two trains for safety. If two curves on a time-
distance chart should touch each other, it would indicate a collision.
The distance between different train curves on a chart gives informa-
tion regarding the kind of signal and brake systems that must be used
to give the desired degree of safety in operating the road.
CHAPTER V
CURVE PLOTTING
INFORMATION may be charted in many different ways. Under
present conditions, if six men were given a set of figures and asked
to chart these figures, the six resulting charts would be widely
divergent in method. Though variety in method of charting is some-
times desirable in large reports where numerous illustrations must
follow each other closely, or in wall exhibits where there must be a
great number of charts in rapid sequence, it is better in general to use
a variety of effects simply to attract attention, and to present the data
themselves according to standard well-known methods.
In Fig. 66 the attempt to give a spectacular scheme of presentation
seems to have overshadowed everything else in the mind of the illus-
trator. Though a striking architectural design has undoubtedly
been obtained, the chart means nothing, for it is impossible of inter-
pretation. No scale has been used in either the horizontal or the
vertical direction, as can be seen by comparing the figures on the block
for 1830 with the figures on the block for 1840. Even if some scale
had been used in making up this chart, the general scheme is such
that the reader would hopelessly flounder in trying to reach an accu-
rate interpretation.
Fig. 67 puts the data given in Fig. 66 in the form of horizontal
bars. Note that the values which the bars represent are given inside
of the bars, for reference purposes. In order to make the shape of
each bar stand out distinctly, gray dots were used which permit the
figures representing the values to be read through the shading. This
is an interesting attempt, but it is not satisfactory as a general scheme.
Though Fig. 67 gives the data much more clearly and far more accu-
rately than Fig. 66, the method is not satisfactory because it is diffi-
cult for the eye to follow the ends of the different bars in order to
judge the increase made from decade to decade. The best method
69
GRAPHIC METHODS
134
222
1830
1840
318
1850
687
I860
829
1870
1504-
!88O
164-7
1690
2224
I9OO
The Philadelphia Commercial Museum
Fig. 66. Commerce of the United States since
1830. The Sum of Annual Exports and
Imports. Values are given in Millions of
Dollars
Such a chart as this is worse than none. There is no scale
in either direction. The block for 1830 is drawn with a
larger area than the block for 1840 which represents a
larger quantity. Compare with Fig. 67 and Fig. 68
CURVE PLOTTING
71
IB30 EJ3*I
IB9O I"'-- '-•'-..- .:.. '..•:•• -• ••- ; •-...•••' : IS47 : O ' - : . •' — :'-\/ •• 1
reoo [15 ••-••••'• -••••••• '.:••• ;zg-»a\ • -j
SB
Fig. 67. Values of Annual Exports and Imports
of the United States. Figures are Given
in Millions of Dollars
This chart is drawn to scale from the data given in Fig. 66,
to show the use of horizontal bars for work of this nature
of the three is followed in Fig. 68, where the data from Fig. 67 are
plotted in the form of a curve. The curve method brings out all
the information in less space and in clearer form than does the block
system in Fig. 66.
An understanding of
how to plot curves and of
how to read them should
be part of the equipment of
every business man, just
as it is of every engineer,
physician, biologist, and
statistician. The general
scheme of curve plotting
is so simple that instruction
in it should be given as part of the work in elementary arithmetic in all
public schools. Children over ten years of age can do plotting and
can understand simple curves like that of Fig. 68. Curves are usually
plotted on co-ordinate paper already ruled in squares, so that the person
doing the plotting need not take
the time necessary to rule the
paper. For reports, for illustra-
tions of magazine articles, or for
advertising, it is ^ordinarily better
to rule by hand a small area such
as is shown in Fig. 68 so that the
spacing of the ruling may suit ex-
actly the data which it is desired
to plot.
In Fig. 68 we have data avail-
able only by decades, from 1830 to
1900 inclusive. Lines are drawn
vertically for each decade. The
scale need not run above 2,300, for
the largest figure to plot is 2,244
millions. A suitable scale is secured
by using one line for each 200 millions. After the background ruling
has been drawn, the figures at each census are laid off to scale, on
the proper vertical lines to represent census years, and a dot is
placed on each vertical line at that vertical distance which represents
MlLUONS c
or *
DOLLARS
22OO
2OOO
1800
16OO
1AOO
12OO
1OOO
eoo
60O
4OO
2OO
O
\ N no f* 0> 0 5 ^
) W £ 0 N S I
2d««>co;!:S?r
,
/
/
/
/
+**^
/
/
/
s
^
/
r
^j_
SB
1830
'5O '6O '7O 'SO 'SO 19OO
Fig. 68. Value of Annual Exports and
Imports of the United States. Fig-
ures are Given in Millions of Dollars
This curve is drawn from the same data as Figures
66 and 67. The curve shows the changes
from decade to decade more vividly than do
the horizontal bars of Fig. 67
72 GRAPHIC METHODS
the data according to the scale chosen. Thus the figure 222 for the
year 1840 would be indicated as a dot on the vertical line for 1840
slightly above the place where the horizontal scale line for 200 crosses
the chart. After the dots for decade years have been placed on the
vertical lines, the dots are joined with a heavy line and a curve
appears.
The curve of Fig. 68 shows the changes from decade to decade
much better than the bars of Fig. 67. It can be seen at once from
the curve that the greatest gain in any decade was between 1870
and 1880 when the increase was three and a half divisions on the ver-
tical scale. The bars in Fig. 67 have no horizontal scale to measure by
and the comparison between census years is accordingly more difficult.
When plotting any curve the vertical scale should, if possible, be
chosen so that the zero of the scale will appear on the chart. Other-
wise, the reader may assume the bottom of the chart to be zero and
so be grossly misled. Zero should always be indicated by a broad
line much wider than the ordinary co-ordinate lines used for the
background of the chart.
In Fig. 68, it will be noticed that figures are given at the top of
the chart to represent the value for each point plotted on the curve.
The use of figures at the top of the chart in this manner is very de-
sirable. The figures are in plain sight, so that anyone desiring to
know the value of any point on the curve can look above the point
to get the actual figure wanted, without having to read from the? scale
at the left-hand edge and then estimate roughly the value for any
point which happens to fall in a space between two horizontal lines
of the scale. Reading from the figures at the top of the chart permits
any desired figure to be obtained more rapidly and much more accu-
rately. In addition to this, the figures are recorded in such manner
that they may be quoted for use elsewhere by anyone who may wish
to make use of the data in a speech or in a written article in which
the chart itself cannot be used.
It would be a desirable thing if in all curve charts the figures for
the horizontal scale were placed at the bottom of the chart rather than
at the top. Many illustrations in this book, taken from publications
of excellent standing, show dates (such as years, months, etc.) at the
top of the chart. If the horizontal scale were always placed at the
bottom, the standard arrangement would be a convenience to the
reader and would give the additional advantage that the top of the
CURVE PLOTTING
73
DOLLARS
4OOO
chart would be free for a numerical statement such as is found at the
top of Fig. 68.
The scales of any curve chart should be so selected that the chart
will not be exaggerated in either the horizontal or the vertical direc-
tion. It is possible to cause a visual exaggeration of data by care-
lessly or intentionally selecting a scale which unduly stretches the
chart in either the horizontal or the vertical direction. Just as the
English language can be used to exaggerate to the ear, so charts can
exaggerate to the eye.
. p OgOSrHOSOOlMCSN^
A curve permits of finer e * S 1. I 1 • 1 1 i 1
interpretation than any
other known method of
presenting figures for anal-
ysis. Fig. 69 gives some
information which many
persons might not fully
grasp if only a column of
figures were used to indicate
the average yearly earnings
of Princeton graduates. The
fairly uniform slope of the
curve for the first six years
after graduation indicates
that the men were receiving
almost uniform raises in pay each year. It must be remembered that a
straight-line curve simply indicates that the amounts of the increases
year by year are uniform in numerical value. If a curve were started at
the lower left-hand corner of the chart and drawn diagonally across each
of the rectangles of the chart, it would be seen at once that there
would be a straight line indicating an increase in salary of $500 per
year. With such a straight line across the chart, the increase in salary
for the first year would be $500. As compared with a zero beginning-
wage there would be an increase of an infinite percentage at the end
of the first year. The next year the increase would again be $500.
Compared to the $500 salary, the increase would be 100 per cent.
The third year the increase would be $500, and compared to a $1,000
salary the increase would be only 50 per cent. A curve of uniform
slope on any chart of rectangular co-ordinate lines indicates only that
there has been a uniform increase or decrease in actual numbers, not
Fig. 69. Average Income of 155 Princeton Grad-
uates of the Class of 1901 for Ten Years After
Graduation
Note the effect of the 1907 panic on incomes in 1908
74
GRAPHIC METHODS
VOtues given in Millions of DolUtt
•PRODUCTION
a uniform rate of change on a percentage basis. A plotted line repre-
senting a uniform rate of increase from year to year on a percentage
basis may be seen in the curve given in Fig. 121.
The untrained reader of
curves will probably not be
able to tell instantly what
made the flat portion of the
curve in Fig. 69 during the
year 1907 to 1908. One of
the chief advantages of the
curve method of presenting
information is that a curve
forces one to think. A
little thought here will at
once bring out the fact that
the flattening of the curve
was caused by the 1907
panic. Though the panic
started in October of the
year 1907, the year 1907
was really one of the most
prosperous years the coun-
try has ever known. It
would be more fitting if the
panic were called the 1908
panic, since the main effect
of the panic came in 1908
rather than in the year
1907. It can be seen that
the Princeton men had
their incomes reduced dur-
ing the year 1908 so that
the average fell below that
of 1907. By looking along
the curve it will be noticed
IMPORTS
as s
n
iflh
EXPORTS
Q Q o o o o
S Sv (2 it o ft
Cotton Goods
The Philadelphia Commercial Museum
Fig. 70. Cotton Goods Production, Import and
Export for the United States. Values are
Given in Millions of Dollars
The order of years here reading from right to left gives the
first impression that production is decreasing. Compare
this illustration with Fig. 71
that though there was a larger yearly increase in salary after 1909,
salaries at the end of 1911 had not attained the point which it
would seem they would naturally have reached if no panic had
occurred at a time so shortly preceding this date.
CURVE PLOTTING
Milllor
Dollar
36O
In Fig. 70 vertical bars have been placed touching each other,
with the earlier years at the right. The whole arrangement of the chart
is extremely poor and also misleading. In Fig. 71 the data of Fig.
70 have been replotted. The most striking thing about Fig. 71 is
the falling off in the rate of increase of production in the decade
between 1870 and 1880. The shape of the curve at once starts a train
of thought in regard to tariff legislation and other conditions which
may affect the manufacture of cotton goods.
- It will be noticed in Fig. 71 that we have four curves, while only
three sets of bars were given in Fig. 70. It is evident that if we add
production and imports and then deduct exports, we will have a fair
indication ol consumption if the amounts remaining in warehouses,
etc. (which are probably a negligible percentage of the whole con-
sumption) are excepted. Note that the import and export curves follow
each other in general form,
though the export curve
fluctuates on a percentage
basis 'much more rapidly
than does the import curve.
Remember that in the fluct-
uations of two curves like
these, the change from year
to year must be judged
from the zero base line
rather than from the slope
of the curves themselves.
The drop in the export
line from 1860 to 1870 was
almost one-half, while the
drop in the import line for
the same period was much
less than one-half, even
though the import line
does show the greater slope
downward.
In Fig. 72 we have an example of what not to do in charting.
The main effect of the circles is to give one a headache without per-
mitting any accurate comparison between the years. The eye does not
easily see each circle as an area. The tendency is to see only rings
Fig. 71. Cotton Goods Production, Import and
Export for the United States
These curves are plotted from the data of Fig. 70, and show
the information in much clearer form
76
GRAPHIC METHODS
between the lines of the circles,
rather than the whole area in-
cluded inside of each circle line.
Fig. 73 gives the data of Fig.
72 in curve form. The heavy solid
line curve shows the changes from
decade to decade as they could
never be interpreted from either
the actual figures or the circles of
Fig. 72. The tremendous increase
in the world's commerce between
1900 and 1910 is of very great
interest, showing the effect which
better means of communication
have brought about as a result of
the splendid increase in scientific
and engineering knowledge.
If one makes comparisons be-
tween the circles of Fig. 72 on a
Billions ot
Dollars
The Philadelphia Commercial Mvsevm
Fig. 72. Annual Commerce of the World,
Imports and Exports Combined.
Shown at Ten-year Periods, 1850-
1910
These circles, drawn on an area basis, are even more
difficult to interpret than the circles of Fig. 38.
The eye is likely to see the rings rather than the
whole areas of the circles. Compare Fig. 73
185O I860 1870 I860 IO3O I9OO I91O
The Philadelphia Commercial Museum
Fig. 73. Annual Commerce of the World,
Imports and Exports Combined.
Shown at Ten-year Periods, 1850-
1910
The solid line is plotted according to the figures
given in Fig. 72. The dotted line shows the
erroneous impression which would be obtained
by the reader if he should interpret Fig. 72 by
the diameters instead of by the areas of the
circles
diameter basis rather than on the
area basis to which the circles were
drawn, one gets an interpretation
like that indicated by the dotted
line in Fig. 73. By comparing the
dotted line with the solid curve
the reader may see the extent of
the error which arises if circles are
compared on a diameter basis after
being drawn on an area basis.
Fig. 74 gives a good idea of the
utility of the curve method for
showing concisely a large quantity
of data. If the figures for the price
of cement had been expressed in
dollars and shown in a long numer-
ical column, there would be very
few readers who would take the
CURVE PLOTTING
77
trouble to follow the table of figures and notice the fluctuations from
year to year. The curve, however, gives all the variations in price
at a glance and shows in most striking manner the great reduction
which occurred in the price of cement as manufacturing facilities im-
proved and increased. A curve of this kind greatly stimulates thought,
for one immediately wishes to know the cause of each of the peaks
and of each of the valleys in the curve. One gets a vista of recurring
periods of financial boom and of financial depression, and a glimpse
of such factors as new developments in methods of manufacturing
cement and the constantly increasing demand for the product.
If the reading of curves were understood by the average educated
person, it would be possible to use, in almost any kind of magazine,
advertising illustrations on the order of that shown in Fig. 75. Since,
however, curves are not
widely understood at
present, this type of
advertising must now
be limited chiefly to
the technical journals
read by engineers and
others who understand
curve interpretation.
It is really a calamity
that curves are not
more widely under-
stood. Advertising men
are now frequently un-
able to convince people of their argument simply because they have
no language by means of which figures can be made interesting or
even intelligible when expressed in an advertisement of limited size.
The author ventures to predict that it will be only a very few years
until curves are so widely understood and used that they may be
presented advantageously in any high-grade advertising pages.
It would be almost impossible to give a clear idea of the flood
indicated in Fig. 76 if only columns of figures were used. With the
curve it can be seen clearly that the stream rose very rapidly and
subsided rapidly, so that the stream was down almost to normal
level within forty-eight hours after the beginning of the flood. This
curve was probably plotted from flood-gauge readings taken once an
. M BULK a MIU.
Li Ji HJLfi
t
1
^
s»,
V
V
\
I
5
s
«"• ua
§M
M
«
*°,
Fig.
, 1
7
[ k
'4
i
I
— |
>r
i
ic
S
es
i
(
i
>f
c
«
e
» i
tn
1
er
! \
it
1
I
1 i
>e
i i
i?
B
5
ar
*»
-^
i \
re
n
1,
/
i]
i
VTL
i
m
B
Dt
111
i
i *
ita
k
! i
'c
£
$ '.
Mi
it
ago
the
Mill, from 1880 to 1910
Columns of printed figures or a series of vertical bars could not por-
tray this information as vividly as it is brought out by the curve
shown above
78
GRAPHIC METHODS
hour, or even more frequently. The curve, therefore, was plotted
on much more numerous points than are indicated by the vertical
lines of the horizontal scale. Frequent observations of the gauge
height and the numerous points plotted on the curve in Fig. 76 ex-
plain those fluctuations in the line of the curve which occur in the
spaces between the vertical lines. Ordinarily a chart is sufficiently
accurate if straight lines are drawn from point to point of the plotted
data for a curve, without attempting to make a smooth, flowing line.
Fig- 75- Advertising Illustration used in a Technical Magazine, with a Heavy-type
Statement Proclaiming that "3000 Central Stations hi the United States need a
High Grade Gasoline-Electric Generating Set"
The black areas indicate the portion of the 24-hour power-house load for which the gasoline engine would
be used
The curve looks smooth in this illustration simply because the gauge
readings were taken so frequently that the nearness of the many
points made the lines joining them appear curvilinear rather than
angular. Such a smooth curve would not have resulted if gauge read-
ings had been taken only every six hours and the chart made by con-
necting with straight lines the points plotted for the data obtained at
these longer intervals.
Another flood curve is shown in Fig. 77. The speed with which
the water ran off the territory drained can be judged by the shape
of the curve. It is not, however, safe to compare the shapes of the
curves in Fig. 76 and Fig. 77 without noticing that in Fig. 77 we have
one day represented by a space approximately the same as the space
used in Fig. 76 for only six hours. If the curve of Fig. 76 were plotted
on the same horizontal scale as the curve of Fig. 77, the flood would
appear to be much more severe and rapid than it appears from Fig. 76.
CURVE PLOTTING
79
30
c
$20
g>
'o>
r
4)
g
o
Noon Noon Noon
3ept.6th. Sept. 7th. Sept. 8th.
Time in Hours
Engineering Record
Fig. 76. Curve Showing Duration of a Flood, September 16, 1909,
in the Canadian River, New Mexico
This curve was first plotted on a paper having co-ordinate lines close together. For
ease of reading, the intermediate lines were omitted from the magazine illustration
In general, it is unwise to compare the shapes of two curves unless
they are plotted to the same scales, both horizontal and vertical.
The curve of Fig. 77 is misleading because the scale does not begin
at zero. Only the peak of the flood is shown, with no zero line from
which to judge the
extent by which
flood exceeded
normal flow of
120000
100000
-25
80000
60000
40000
20000
-5
26 27 28 29
March. 1913
31
2
April
Engineering Record
Fig. 77. Flood in the Hudson River at Mechanics-
ville, N. Y., March, 1913
Note the different scales at the right and the left by which the
curve may be interpreted. This chart is misleading because the
scales do not begin at zero
the
the
the
river. If the co-ordi-
nate lines were drawn
so as to show the zero
line, the base of the
chart would be about
^8 inch lower than it
appears in Fig. 77, and
the whole curve would
make a different im-
pression. The omission
of the zero line in charts
of this kind is partic-
ularly irritating, yet it is a very common error made by persons
drawing charts.
Note that in Fig. 77 the curve can be read from two distinct scales,
one scale on the left side of the chart, and a different scale on the
80
GRAPHIC METHODS
right side of the chart. If only one scale is used, ft should be placed
at the left-hand side of the chart. In very large charts it is some-
times desirable to repeat the scale at the right-hand side as well.
Where two different units of measurement are used in the scales,
the units should be carefully named so that there will be no danger
of the reader's using the right-hand and the left-hand scales inter-
changeably as though they represented the same unit.
CITIES Charts like that shown in
Fig. 78 are quite frequently
used in public health reports.
It is difficult to see how such
an unsatisfactory type of
chart ever came into general
use, unless it was because
there are twelve months in a
year and twelve hours on the
face of a clock. If the death
rates for the different months
of the year were plotted in a
curve, using rectangular co-
ordinates, the data would be
just as easy to read and to
understand as when shown by
the radial scheme (polar co-
ordinates) of Fig. 78. There
would be the additional ad-
vantage that the rectangular
United Slates Statistical Atlas of the 1900 Census
Fig. 78. Death Rate from Consumption per
1000 Inhabitants for Each Month of the
Year in Cities of the United States
This type of chart should be banished to the scrap heap.
Charts on rectangular ruling are easier to draw and
easier to understand
method would be more widely understood than the circular method
of Fig. 78.
Though a chart in the form of Fig. 79 might be justified in the
Sunday supplement of a newspaper where an untrained audience must
be reached, it is much better to use a curve in the form of Fig. 80
whenever a trained audience is assured. The most interesting thing
about Fig. 79 is the slanting line which gives an unusual optical illusion
if observed under artificial light, especially with a bare gas flame.
The slanting line then appears blue, although it is printed black like
the horizontal bars of the chart.
The dotted line in Fig. 80 corresponds to the slanting line of Fig.
79, and represents a progressive average of all the points on the curve
CURVE PLOTTING
81
above. The dotted line, of course, coincides with the solid line at the
first point where there is only one point to consider in the average.
Figures for the dotted line are obtained by averaging the figures for
the first two years, then the first three years, then the first four years,
etc., until the last point on the dotted line represents an average for
all the points on the solid line.
Fig. 80 is worthy of attention as a model of good practice which
may be studied carefully by anyone just beginning to plot curves.
Pittsburgh and Lake Erie Railroad
Fig. 79. Yearly Average of Revenue Tons per Train Mile on the Pittsburgh and Lake
Erie Railroad. The Slanting Line Shows a Progressive Average
If this illustration is observed with artificial light, an interesting optical illusion may be noticed in that the
slanting line appears blue in color
The use of horizontal bars here gives a chart less easy to interpret than the curve shown in Fig. 80 for these
same data
82
GRAPHIC METHODS
^ «>
.^^U^io A*na<0a<'>aoa*tnnu>00f')<<)f*«-9--'N<0r»N<9Nr»0>(a
^ vrf> • • ~ «t • i $ 9 • 9 9 3 * • 9 9 • • 9 • * * • • * ~ ** * « * • 5 • •
^.^r 5'5 ii 5 ti • * ..il * Jl * 4 * *•• T * * * * si •». •» K i» • o o * g o 5-. • i
^W) 11,11 — i — iiiiiiiiiiiiiiiii777777777
Fig. 80. Yearly Average of Revenue Tons per Train Mile on the Pittsburgh and Lake
Erie Railroad. The Slanting Line Shows a Progressive Average
Here we have the data of Fig. 79 plotted in a curve which can be interpreted easily and accurately
This chart may be considered a model of good practice in curve plotting. All of the work, including the
lettering, has been done by hand, thus insuring better results than can usually be obtained from printing
The following features of Fig. 80 are pointed out for the benefit of
anyone who may have curves to plot:
1. The zero line is a much broader line than the co-ordinate
lines.
2. Heavy lines are not used at the right- and left-hand edges,
since the chart does not start or end at the beginning or end of
time.
3. All lettering is so made that it can be read horizontally or
from the right-hand edge of the sheet.
4. Years are given with four figures for every tenth year
ending in zero. Other years are indicated with two figures so that
they may be more quickly read.
CURVE PLOTTING 83
5. All letters and figures on this chart were made by hand,
showing the perfection which may be attained by practice in
lettering.
6. The curve itself stands out clearly from the co-ordinate lines.
7. Figures at various points along the curve indicate matters
which are worthy of special notice. Foot notes are not given
here, however, as they are only of highly technical interest.
8. Figures for the values of points on the main curve are given
at the top of the chart immediately above each corresponding
point on the curve. Values may be read correctly from the upper
figures rather than guessed at by estimating them roughly on the
left-hand scale.
9. The statement "Revenue Tons per Train Mile" at the upper
left-hand corner is purposely printed diagonally so that it may
serve as a heading for each of the two columns of figures, one at
the left and the other at the top of the chart. The diagonal ar-
rangement gives a neater effect than can be obtained otherwise.
10. Though figures for the dotted curve could be shown at
the top of the chart the dotted line is of only minor interest here.
It is accordingly best to avoid the two columns of figures at the
top in order that the figures for the main curve may stand out
more prominently.
CHAPTER VI
CURVE PLOTTING CONTINUED
THERE are so many different applications of curves and such
varied yet convenient methods of plotting curves, that it seems
worth while to take up some of these in detail, and point out
certain advantages and disadvantages of different curve-plotting
schemes.
Practically all curves display relations existing between different
sets of data which we may call " variables". One of the variables
is used as a standard or measure by which to interpret the facts under
consideration, and it may be called the "independent variable". The
other variable, which is interpreted from the independent variable, is
called the "dependent variable". For example, in a bacteriological
examination of a pond at varying depths, distance below the surface
would be the independent, and number of bacteria per cubic centimeter
the dependent variable. In a seasonal gauging of a stream the dates of
observation would be the independent and cubic feet per second of
flow the dependent variable. Sometimes we consider more than two
variables simultaneously, and we then have two or more independent
variables from which to consider a dependent variable.
It is difficult to make a general rule for determining in any case
which is the independent variable and which is the dependent variable.
The decision depends entirely on how any set of data is approached
and on the habits of mind of the investigator. When time is one of
the variables it is usually, but not always, the independent variable.
If we consider values or quantities at different dates, as in Fig. 80,
time is very obviously the independent variable. If, however, we are
interested in the length of time required to do different operations, as
in Fig. 85, Fig. 86, and Fig. 87, our data are expressed in length of
time and time is the dependent variable. This example is an excep-
tional case and it is named here only to show that, although time is
84
CURVE PLOTTING 85
ordinarily the independent variable when it enters into curve plotting,
nevertheless there may be occasions when time is the dependent
variable, and charts should be plotted accordingly. It is important
that the person drawing a chart should in each case distinguish be-
tween the independent variable and the dependent variable, for this
distinction affects the whole arrangement of the chart.
It should be a strict rule for all kinds of curve plotting that the
horizontal scale must be used for the independent variable and the
vertical scale for the dependent variable. When the curves are plotted
by this rule the reader can instantly select a set of conditions from
the horizontal scale and read the information from the vertical scale.
If there were no rule relating to the arrangement of scales for the
independent and dependent variables, the reader would never be
able to tell whether he should approach a chart from the vertical
scale and read the information from the hori-
I7.00O , - - -
zontal scale, or the reverse. It charts are
always plotted with the independent varia-
ble as the horizontal scale, there need be no
question in the reader's mind as to how he
should interpret the chart. The rule for scale
arrangement is not always followed, and a
few examples are shown here to indicate the
difficulty of interpretation which the reader
may have just because a rather simple prin-
ciple of curve plotting has been neglected,
^l^o' ,i0r.UIr,,t!^0rw In Fig. 81 the depth of the water has
rcrici per v/ u Die v/ciiii~
meter of Hudson River been plotted downward from the top of the
Water at New York at cnart so that the reader may get the impres-
Different Depths below . „ -, ,.» p ..
the Surface ' Slon °* measurements taken at different dis-
tances below the surface of the water. In
making the tests which are represented in Fig. 81, different depths
below the surfaces were selected and the bacteria determined from
the water samples taken at these depths. The depth is here the in-
dependent variable, and bacteria per cubic centimeter the dependent
variable. The decision as to which is the independent variable and
which is the dependent variable rests entirely on how the problem is
approached. Numerous samples could have been taken at different
depths, and then a curve plotted to determine the depth at which
certain numbers of bacteria per cubic centimeter were found. In
i sston
86 GRAPHIC METHODS
such a case, bacteria per cubic centimeter would be the independent
variable and depth would be the dependent variable. This sort of
problem may be attacked from either one standpoint or the other,
and it is just a question of convenience as to which method is used
and which variable is made the independent variable. Though the
problem can be stated in such manner that either one variable or the
other can be made the independent variable, after the statement
has been made the chart should be consistently drawn so that the inde-
pendent variable will be used as the horizontal scale and the dependent
variable as the vertical scale.
As Fig. 81 is shown it is necessary for the person interpreting the
chart to select from the vertical scale some number of feet below
the surface and then read the number of bacteria per cubic centi-
meter by the horizontal distance to the right. It is only after some
little puzzling that the reader will notice that the scales for the
variables have been reversed and that the chart has been practically
turned on its side. How this chart would appear if the horizontal
scale were used for the independent variable may be judged by turning
the book and looking at Fig. 81 from the left-hand side of the page.
Though it is easy to see why the person making Fig. 81 happened to
arrange the chart in the manner shown with the variables reversed,
the gain due to showing depth below the surface in the vertical direc-
tion does not make up for the possibility of misinterpretation which
results because of the neglect to follow standard practice.
In Fig. 82 we again have depth plotted downward from the top
of the chart. . As we wish to determine the velocity of the stream at
different depths of water, depth is the independent variable and
velocity is the dependent variable. The arrangement of Fig. 82 is
not as objectionable as Fig. 81, for the upper half of the illustration
shows quite clearly in pictorial form that the subject under considera-
tion is a stream having a channel shaped as shown, with widths and
depths as indicated by the two scales. In the bottom portion of the
diagram the scale of depths downward relates very definitely to the
upper portion of the illustration so that the reader cannot easily go
astray. Notice that the curves for the velocity of the water are each
plotted on a separate vertical line which serves as zero line. The
curves for velocity begin at various points depending upon the thick-
ness of the ice, as will be seen from the upper portion of the chart.
There is, of course, no velocity in that portion of the stream which
CURVE PLOTTING
87
Distances in feet
40 50
0
I1
.£2
8
•s3
o.
2 4
I
1*
ta
« 6
O
7
VERTICAL VELOCITY CURVES
Note Numbers at totf of curves indicate measuring points
Numbers at bottom of curves indicate mean velocity in toe vertical
?o
30
35
40
45
5
0
55
60
Bf
6!
>
70
\
\
)
\
\
[
\
\
\
1
1
~1
80
85
J
.43
t
1
}
\
\
\
C
c
i
<
/•
(
.47
J
S
1
/
I
j
J
C
c
c
/
3
/
04
J
f
I
i
t
/
/
j
.63
_y
///
J
/
/
°l
^
il
1
2
.- — /
.52
/.Z9
1.49
1.45
_J
1.34
^r
/./j
Horizontal divisions represent one foot per second velocity
Engineering News
Fig. 82. The Velocity of Water in Different Portions of a Stream Flowing under Ice
The horizontal scale at the top of the illustration shows points where velocity measurements were made
through holes in the ice. Velocities at different depths are indicated by the curves in the lower half of
the chart, each curve being plotted to the right of a vertical zero line which corresponds with some hole
in the ice. Lines are drawn in the upper portion of the chart showing different points in the stream
where velocities are the same
is frozen. The velocity curves end abruptly at the bottom of the
stream. It will be seen by reading velocities horizontally from the
different zero lines from which the curves are plotted that the velocities
are considerably greater in the center of the stream than they are
near the banks or the bottom. This is natural, as the friction of the
earth bottom and sides, as well as the friction of the ice at the top,
causes the water to be retarded and the velocity lessened. In the upper
portion of the illustration lines are drawn through all those points
in the stream cross-section which have the same velocities. The lines
are similar to the well-known isothermal lines on a weather map show-
88
GRAPHIC METHODS
ing where the temperatures are the same. From these lines it can be
seen instantly that the highest velocity is at the center of the stream,
as far away as possible from retarding influences. Velocities gradually
grow less as the sides, the bottom, or the ice at the top are approached.
8
9
8
1 ^'' -^'^
^ -• ' ^o*" ^ - '
0 X
*E-^^'
S X
.!'*!•'''
3" - • •J'f
8 ,t'.'.
! s* ;.•'':
S'" '* ' ,.
8 ,;' c^>^
' < ' ' '
° <' "»;S':
§ --;;'"--;-;.:!1"- :
™ ' • ! * '
8-- <'«£***'.
.50 3.OO .90 4.00 .90 5.0O JO
RELATIVE VALUE IN DOLLARS
Courtesy of Data, Chicago
Fig. 83. Relative Value of Different Coals as Compared to Anthracite Coal
The price of anthracite coal is here the "independent variable" since it is the standard or measure by which
the other variable is judged. The price of anthracite coal should have been made the horizontal scale
of the chart. See Fig. 84
Fig. 82 is an interesting piece of work and the method used in charting
is justifiable, even though in this case, as in the preceding, the
independent variable is plotted downward and the dependent variable
is plotted horizontally.
2 34 5 6 T G 9
Price of Anthracite Coal — Dollars
10
it
Fig. 84. Relative Value of Different Coals as Compared to Anthracite Coai
With the arrangement shown here the curve lines for different coals appear in their correct position. Illinois
coal is at the bottom instead of at the top. The heavy line here drawn for anthracite proves at a glance
which fuels are better and which poorer than anthracite
CURVE PLOTTING 89
Fig. 83 is intended as a comparison between different kinds of
coal from the standpoint of actual heating value. At the first glance
at this chart the reader sees that the line for Illinois coal is above the
other lines, and he is apt to draw the conclusion that Illinois coal is
better than anthracite, coke, or Pocahontas coal. It is only after
some puzzling over the chart that one notices that the whole chart
has been drawn in reversed order. We are considering what the
relative values of other coals may be if we know the value of anthracite
coal. The whole scheme of reasoning begins with the "price of an-
thracite coal." The "price of anthracite coal" is the independent
variable and should be plotted horizontally, with the "relative value
in dollars" plotted as the vertical scale. The reader may get a correct
impression of the chart in Fig. 83 if he will turn over the page and
read the chart by holding the page up to the light in such manner
that the zeros of the two scales appear at the lower left-hand corner.
When this is done, it will be seen that the relative value of Pocahontas
coal exceeds each of the other fuels mentioned and that Illinois coal
comes not at the top of the list, but at the bottom of the list in so far
as fuel value is concerned.
Fig. 84 has been drawn with the "price of anthracite coal" as the
horizontal scale, where it belongs because it is the independent vari-
able. The lines for different fuels now appear in their correct order,
and the reader sees at a glance that Pocahontas coal has more fuel
value than anthracite coal. Notice that a heavy line has been used
for the curve line drawn for anthracite coal. As this line is the standard
by which the values are compared, it seems best to give it prominence
on the chart. The position of other curve lines above or below this
line shows instantly whether the fuels are better or worse than anthra-
cite in relative value.
In Fig. 85 an effort has been made to show detail time-studies
by the use of curves. There is an error here, however, in that the curve
has been arranged in such manner that the independent variable is
drawn vertically and the information desired as "time in seconds"
must be read off from the horizontal scale. The reader wishes to
know how many seconds are required for any one step or any series
of steps in the whole work. The chart can be interpreted in the accus-
tomed way if the page is turned over, and the diagram read by hold-
ing the page in such manner that the zero on the scale of "time in
seconds" appears at the lower left-hand corner of the chart when the
90
GRAPHIC METHODS
page is held up toward a light. The curve for operator No. 1 then
appears below the curve for operator No. 2 and the chart shows cor-
rectly the relative merits of the two operators. Fig. 86 is a re<
drawing of the data
shown in Fig. 85'.
Here the curves for
the two operators
appear in their cor-
rect relative position,
and it is seen at once
that operator No. 1
is the more rapid
worker, since he uses
less time. With the
independent v a r i -
able made the hori-
zontal scale, a chart
can be interpreted
quickly. If the de-
pendent variable is
used as the horizon-
tal scale the reader is
likely to draw a con-
clusion the reverse of
that the chart was
intended to show.
Opsrotop No.1. Operator No. 2
ations
Adjusts
and
smoothes _
label --f-y
Puts :::'::
label on 1 —
package [
Replaces f-
brush 1
Covers " — 1~.~ i '
m $m
II
::3::
L;-4/:i
:::::?::
:::2±E:::::::::::::::::
A-— ^-r-
i
a
0
label with — t i-~
giue :::j|:: /
:^:::ji:::::
Brings • --i £-
brush to . --^- f
label ?" r 7
wipes ::::L";!.:
brush on *'» '-
glue pot •-- sj!»"- -
Reaches — ^ ! - — - - - — 1
for brush THj' '
Reaches '.it "-
for label 1* 1
O 5 1O 15 20 2
Time in s
5 30 35 40 45 SO
sconas
Aaapuu ji-. . _„ ^..,
Fig. 85. Record of a Detailed Time-Suiuy of Two
Operators Labeling Packages
We are here studying the time for different operations. The names of
the operations constitute the independent variable while time is
the dependent variable. The chart reverses the proper arrangement
of scales and causes the curve for operator No. 1 to appear improperly
above the curve for operator No. 2. Compare Fig. 86
Fig. 87 shows the data of Fig. 85 and Fig. 86 redrawn in the form
of horizontal bars such as were seen in Chapter I and Chapter II.
The relative times for the various operations are shown much more
clearly by the horizontal bars than by the curves used in Fig. 85 and
Fig. 86. The time in seconds required for each operation is given
by detailed dimension lines above each section in the horizontal bar,
and the comparative total time of the two different men can also be
grasped instantly. The total time in seconds for the whole series
of operations is shown by an over-all dimension line above each of
the bars, and the reader, if he wishes, may make an accurate com-
parison between operator No. 1 and operator No. 2 by using a numerical
ratio. A chart of this kind can be very quickly made for ordinary
office purposes if the horizontal bars are drawn on co-ordinate paper
CURVE PLOTTING
and the different areas made to
stand out in contrast by the use of
colored crayons. The actual differ-
ences between the two operators
would show more clearly, operation
by operation, if lines were used join-
ing the ends of the components in
the two bars in a manner similar to
that seen in Fig. 32. The data of
Fig. 85 do not lend themselves well
to presentation in curve form. In
Fig. 85 and in Fig. 86 .the shape
of the curves means nothing, since
there is no numerical scale relating
to the names of operations. Fig.
87 shows a much more satisfactory
method for portraying the data.
In Fig. 88 we have an applica-
tion of curves to advertising in pop-
ular magazines. The curves de-
pict the circulation of a newspaper,
Operations
Fig. 86. Record of a Detailed Time-
Study of Two Operators Labeling
Packages
Here the scales have been properly arranged and
the two curves appear in their correct relative
position on the chart. These data, however,
are not well suited for curve presentation
and they are more clearly brought out by the
bar method used in Fig. 87
*-3-*
^
£.
* 9 >
!•:->
oeconc
. 9
IS
EJ
4k
i i •* i
Oper-
ator
No.2.
1
HI
3
4
6
7
8
Oper-
a-tor
No.t.
*2*
•-3-*
C.^7 »
« 6 "
->t
^2>
stjon
• — 5 — «•
CJi
«-a«
^-3—
. 6 -
i !l ;
iiii
ie.|
3
4
•Bi
7
8
Scale 1 sec. = O.I'
Fig. 87. Record of a Detailed Time-Study of Two Operators Labeling Packages
By this method of presentation the reader may see clearly the relative 'ength of time for different operations
as well as the comparison of total time taken by the two workers. Dimension marks and figures show
conveniently the actual number of seconds required. The different operations have here been given
numbers instead of names. The scale to which the chart is drawn is named
GRAPHIC METHODS
1905 1906
1907
1908
1909
1911
1913
150.000
150.000
The Plain Dealer'* circulation is by far the
largest net paid morning and Sunday newspaper
circulation between New York and Chicago: and
in Cleveland and the retail trading area tributary
to Cleveland — a radius of 75 miles at most- the
Plain Dealer's net paid circulation is double the
net paid circulation of any other Cleveland
morning or Sunday newspaper. Every record
bearing directly or indirectly upon figures above
published or upon any other detail of Plain
Dealer Circulation or Advertising is open to the
most complete and searching investigation to
anyone at any time and without further notice.
70000
EXPLANATION OF CHART
This chart shows the Cleveland Plain Dealer's circulation by
months from February 1905 to June 1913. Each line up and down
represents a month, each line across a thousand copies sold. Note
how the top line indicating Sunday sales, and the lower line indi-
cating daily sales move steadily upward. Observe the steady,
healthy, sturdy growth from the first month to the last — no sudden
mushroom-like gains, no unexplained losses, but a consistently
increasing total affected only by the changing seasons and the bus-
iness health of the whole country.
Cleveland Plain Dealer
Fig. 88. The Use of Curves in an Advertisement to Show the Growth in Circulation
of a Newspaper
It is unfortunate that this illustration was not made so as to show the zero line of the vertical scale. In
advertising work it usually pays to avoid anything which might seem like exaggeration. Omitting
the zero line makes the growth seem more rapid than it would if the zero line were included in a chart
drawn to scale. Though the drafting on this chart might have been better, the application of curves to
advertising deserves commendation
with the object of convincing advertising managers that this par-
ticular newspaper is a desirable one in which to place advertisements
because of the rapidly and steadily increasing circulation. It is sur-
prising that circulation managers of newspapers have not more often
used charts to show circulation, instead of the wordy typed state-
ments so frequently seen claiming great growths in circulation over
a period of months or years. Though Fig. 88 shows a commendable
progressiveness on the part of this particular newspaper in adapting
curves to circulation statements, it seems necessary to point out the
fact that the chart may cause distrust in the minds of some readers.
There is a chance that the man who has advertising to place may feel
CURVE PLOTTING
93
that the chart has been drawn in too optimistic a manner because it
does not show zero at the bottom of the scale. It would have given
a much more conservative impression if the excellent record of circu-
lation growth had been plotted in curves having the zero line shown
at the bottom of the chart, so that the relative growth could be accu-
rately judged visually.
In Fig. 89 a large amount of information has been condensed into
a small amount of space, yet the chart is fairly clear and easy of in-
terpretation. Several ingenious combinations have been included as,
for instance, the arrows that show the prevailing direction of the
wind each day. The chart gives unusually complete information in
a most convenient form for any ventilating engineer or power-plant
manager who wishes to keep careful track of his cost of coal in different
months of the year as dependent upon weather conditions.
DAY OF MONTH
» 10 11 18 13 1< IS 16 17 18 19 80 21 82 83 84 25 26 «T 88 >» »0> »j
SRSCKRCPCSSCPCC PC.S PC /?/?/? PC PCSSSnS
Heating and Ventilating Magazine
Fig. 89. Record of the Weather in New York City for December, 1912
The heavy line indicates temperature in degrees Fahrenheit
The light solid line shows wind velocity in miles per hour
The dotted line depicts relative humidity in percentage from readings taken at 8 a.m. and 8 p.m.
Arrows portray the prevailing direction of the wind
Initials at the base of the chart show weather conditions as follows: S, clear; PC, partly cloudy; C, Cloudy;
R, rain; Sn, snow
Fig. 90 shows an example of double co-ordinate ruling on the
same sheet of paper. The scheme of using double co-ordinates is
not very well known even to engineers and it seems worthy of atten-
tion here. The solid line plotted in the general form of a curve with
a flat space for each month shows the total water consumption in
millions of gallons per day. The total water consumption is read
from the scale of the horizontal lines as for any curve plotted by
rectangular co-ordinates. The slanting lines are drawn after the total
94 GRAPHIC METHODS
number of gallons used per day has been divided by the number of
inhabitants in the district so as to obtain a figure for the average
daily consumption of water per capita. As the population figure used
depends upon census records it may be necessary to get the rate of
growth in the population from records as much as ten years apart.
In Fig. 90 it can be observed that the slanting lines showing the rate
of growth of the city are straight lines, indicating probably that the
census figures were used in the drawing of these lines because yearly
figures could not be obtained. If yearly figures were obtainable the
slanting lines could be extended year by year until they reached
completely across the chart. The rate of growth in population deter-
mines the angle of the slanting lines, the more rapid the growth the
greater the angle of the lines.
The slanting lines are located on the page so that a curve can be
read from either the horizontal lines or from the slanting lines. The
method of locating the slanting lines can be worked out by anyone
who will experiment a little in making a chart of this type. When the
population is known and the total consumption is known, it is only a
matter of division to determine the consumption per capita. After the
slanting lines are once placed upon the chart, the curve can be read
either from the horizontal lines showing the total consumption or
from the slanting lines showing gallons per capita.
Taking the peak for February, 1912, we see that the total con-
sumption averages during the month 142,000,000 gallons per day.
Reading this same month from the slanting lines we observe that the
average consumption per capita daily was 127 gallons. Notice, 'that
while the total consumption in gallons was much larger in February,
1912, than in January, 1909, as seen by considering the horizontal
lines, the consumption per capita in February, 1912, read from the
slanting lines, was somewhat less than in January, 1909.
If we consider the growth in the population of the city of Boston,
it is permissible that the total water consumption in 1912 should be
greater than in 1908. In spite of the large growth of the city from
1908 to 1912, there has been a general decrease in the total quantity
of water consumed. The decrease in total consumption is chiefly
due to the metering of water to individual users, eliminating a large
part of the water waste which formerly occurred because of careless-
ness on the part of consumers. The actual percentages of the services
which were metered in each one of the years considered may be seen
CURVE PLOTTING
95
Diagram
Average Parity Consumption of Wafer:
of MejrvfoJifetti War far A £>ewrroya Board
vn <S(- Whipple.
/Sb
/4a
\
/Jo
t
Courtesy of Hazen & Whipple, New York
Fig. 90. Chart Showing by Months the Average Total Daily Water Consumption in
Boston, and by Months the Average Daily per Capita Water Consumption. Also
the Yearly Average of Daily Consumption Stated hi Total and per Capita
In this illustration the curves may be read from either of two different sets of co-ordinate rulings. Using
the horizontal ruled lines, we may read from the curves the average total consumption per day. By
reading from the slanting lines, the same curves may be interpreted as the average consumption per
capita per day. The scheme of using two sets of co-ordinate rulings is a valuable one. The scale for
"million gallons per day" should, however, have been shown only at the left, with the slanting line
scale for "gallons per capita" placed in the right-hand margin for the sake of -clearness
by referring to the figures near the upper portion of the chart. Note
that in 1908, 21 per cent of the services were inetered, while in 1911,
45 per cent were metered. The proportion of the services metered in
1912 was not known at the time the chart was made and hence is
not recorded.
A little study of Fig. 90 will show that there is a very striking
similarity in the shape of the waves for different calendar years. Water
consumption is high in the winter and again high in the summer months,
with the lowest point each year usually found in November. The
exact amount of resemblance of these waves to each other could be
determined in an interesting manner if a separate curve were plotted
for each year- so that all the curves would be shown one above the
other in the manner seen in Fig. 103.
96 GRAPHIC METHODS
Just how much the total consumption in water has been decreased,
even though there was an increasing population, may be seen by re-
ferring to the dotted line on the chart. This dotted line was plotted
from points which represent the average for the whole of each year.
Thus, the average in 1905 was about 122 million gallons per day and
in 1911 about 113 million gallons per day. There is so great a fluc-
tuation in the main curve from month to month that it would be diffi-
cult to judge accurately whether the average consumption is going
up or down if some such curve as the dotted line were not used. An
average curve line run through a curve in the manner shown by the
dotted line in Fig. 90 is of great assistance in drawing accurate con-
clusions from curves which have much fluctuation.
In Fig. 90, the dotted line, plotted through a point giving the
average for each year, thoroughly eliminates all the fluctuations
which would be so confusing to the reader if he had to study only the
monthly curve. The dotted line shows conclusively by its slant that
the total consumption from 1905 to 1908 inclusive went up just about
as rapidly as the growth of the population would lead one to expect.
After 1908, however, there was a tremendous drop in total consump-
tion, even though the population kept on increasing. In 1912, the
average total consumption per day went up somewhat above 1911,
but yet it did not increase much more rapidly than the slanting line
of the per capita scale might indicate as permissible. Fig. 90 could
have been improved somewhat if the dotted line had been replaced
by a broad black line which would bring the yearly-average curve
vividly to the attention of the reader. The yearly-average curve
really gives the most interesting conclusions which can be drawn
from this chart and it is worthy of greater emphasis to the eye than
is given to it in the chart.
It would have been better if the scale for "millions of gallons per
day" had been placed only at the left-hand edge of the chart in heavy
lettering so the figures would stand out clearly. The scale for the
slanting co-ordinate lines could then be placed at the end of each
slanting line at the right-hand side of the chart. The scale for the
slanting co-ordinate lines is too difficult to find in Fig. 90.
An interesting study could be made from Fig. 90 by plotting a
curve which would show each year the percentage of services which
were not metered, instead of using the figures at the tap of the chart
which show the percentage of services which are metered. A curve
CURVE PLOTTING 97
for the percentages of services not metered should show some similarity
in shape to the dotted line curve in Fig. 90, giving the yearly average
of daily consumption.
When any curve fluctuates greatly, the general trend of the curve
can be most easily determined if the method of moving averages is
used. If data are plotted by months, a moving average is frequently
made to include twelve months. As a succeeding month is included
in the moving average, that calendar month of the preceding year is
dropped out of the average so that the average always includes twelve
months. The moving-average curve is a much smoother curve than
a curve made from the monthly figures, and is accordingly more easily
interpreted. The degree of smoothness of any moving-average curve
depends chiefly on the number of points included in the moving av-
erage as compared with the number of points in one complete wave
or cycle in the data curve, and the moving-average curve is most
smooth if the moving average includes the same number of points
as are usually found in one complete wave or cycle of the fluctuating
curve.
Many curves plotted by weekly or monthly observations show a
complete wave or cycle each year because of the effect of the seasons.
With such a curve it is best to use for the moving average the number
of points included in one year of the fluctuating curve. When, how-
ever, we study curves relating to financial conditions in any country,
we find that there are complex cycles which involve several years.
With such a complex curve considerable care must be used to deter-
mine the average length of one wave or cycle, so that the moving-
average curve may be made as smooth as possible and most nearly
represent the data being studied.
In Fig. 91 the data when plotted by years give such a complex
curve that it is not easy to determine just how rapidly exports have in-
creased. To show the effect of different numbers of points included
in a moving average, curves were drawn with moving averages for
three years, five years, and ten years. Since the distance between
peaks on the curve making one cycle of fluctuation averages more
nearly ten years than three years or five years, the ten-year curve
more closely approximates a smooth curve line than either of the
other twro curves. As a matter of fact, the intervals between peaks
change somewhat so that it is difficult to select any one number of
years as the correct number for use in making up the moving average.
98
GRAPHIC METHODS
'Lj °
M o '•-•
M_l ft 9'
° £ ° >>a
S5IJB
gi°«J
5 | .1*3
O S-gaSg
H 2l|'&
. l'|s°
M 4- O W >-
» S^l
bb.S-S^ j
s^§.r-§
- ^^^ ^
llll
^ x s*2
4? O cfi O
^^"c i
(o*.S »
CURVE PLOTTING 99
The heavy smooth curve was drawn finally by using the points which
represent the averages of the decades and then sketching in, free
hand, a line which gives a smooth curve and removes the waves found
in the ten-year moving-average curve. Notice that the heavy smooth
curve is so drawn through the ten-year curve as to give approximately
equal areas on either side of the smooth curve between that curve
and the curve for the ten-year moving average. The curve for the
ten-year moving average evidently does not give a fair interpretation
of yearly data, because the ten-year average curve shows a peak in
the year 1886 while the data as plotted by years show a valley for that
year. The peak in the ten-year moving-average curve in 1886 was
caused by the number of years included in the moving average not
being a true representation of the length of one full cycle. The length
of the cycle changes from time to time, so that no one selected cycle
length is satisfactory for the whole curve. The heavy curve sketched
in by hand is the fairest approximation to show the trend of the fluc-
tuating curve as a whole.
In Fig. 91 the points on any smoothed curve are plotted midway
horizontally in the range of years included in each moving average.
It is on this account that the smoothed curves, though all plotted
from the same data, do not seem to end at the same year at the right-
hand side of the chart. Though it is good practice to plot smoothed
curves in this manner with each point midway in the horizontal range
of the points included in any moving average, there are times when
it is not desirable to have the point on the moving-average curve fall
behind the latest point on the data curve. For operating records in
industrial work, the moving-average curve is convenient to show an
average for the preceding twelve months or for any other length of
time immediately preceding. With such curves it is usually best to
have the last point of the moving-average curve plotted on the same
vertical co-ordinate line as the last point of the data curve.
Index numbers are used very commonly in the study of facts
relating to the prices of commodities over a long period of time. When
making comparisons by index numbers, conditions are selected which
as nearly as possible represent the normal or typical conditions for the
subject under consideration. The figures for other dates are then
compared with the figures representing the normal conditions, by work-
ing on a percentage basis so that the figures for the normal conditions
are taken as unity or 100 per cent. Figures for the conditions to be
100
GRAPHIC METHODS
compared with the normal are expressed in percentages, making the
increases above normal in figures above 100 per cent and decreases
below normal in figures below 100 per cent. Unfortunately, the reader
not familiar with index numbers may not realize that a chart relating
to index numbers should be read from the 100 per cent line rather
than from the base of the chart. It is very common to find a chart
relating to index numbers so drawn that the chart does not extend
to the zero of the
vertical scale. Such
a chart may give a
false impression of
much more violent
fluctuation than
would be interpreted
from a chart plotted
on the usual co-or-
dinate field and
showing the zero of
the vertical scale.
Fig. 92 is taken
from the United
States Government
Crop Reporter, a
magazine widely dis-
tributed to farmers.
. Untied StateslGovernment Crop Reporter
Fig. 92. Fluctuation in the Price of Eggs in the United
States as Compared with the Average of the Monthly
Figures for the Preceding Four Years
An untrained reader may not realize that this chart must be read from
the line representing 100 per cent. Charts for index numbers, where
the fluctuation is compared with 100 per cent, should have the 100
per cent line made broad, and a wavy line should be used at the
bottom of the chart unless the zero of the scale is shown. An alter-
native arrangement is shown in Fig. 93
It has been the hope of this magazine to give producers of agricultural
products an opportunity to study the price records of previous years, so
that they may, in so far as possible, sell at the time of the year when
prices are the highest. It is much to be doubted whether the average
reader of charts like that seen in Fig. 92 would realize that the 100 per
cent line must be used as a basis for interpreting the chart. The 100 per
cent line has not been made any heavier than the other lines on the
sheet. A man who had been at all accustomed to reading charts
having zero at the base of the chart would be apt to read Fig. 92 as
though the bottom line were the zero from which the curve had been
drawn. On such a basis, he might think that the price of eggs in
January, 1912, was more than eight times the price in July, 1911.
Such a conclusion would, of course, be entirely unwarranted by the
actual figures.
CURVE PLOTTING
101
Where charts for index numbers are made on the 100 per cent
basis, it would seem best to have a broad line for the 100 per cent
line. If there is not room to extend the co-ordinate field down to the
zero of the vertical scale, the co-ordinate field may be shown broken
off with a wavy line at the base indicating to the reader that the bot-
tom of the chart is not a zero line, and that the chart must be read on
the 100 per cent basis.
Fig. 93 was drawn from the data of Fig. 92 as a suggestion for a
type of chart which might be used where an untrained class of readers
must be reached. By plotting increases above the zero line and de-
creases below the
zero line, a chart
is obtained which
needs little space
and which never-
theless is on a large
scale, giving a
great amount of
detail so as to per-
mit accurate read-
ing of all the vari-
ous points on the
curve. There is
very small chance
for any untrained
reader to misin-
terpret a chart
made by the gen-
eral method used
in Fig. 93.
94 is essentially a chart relating to index numbers. The
Fig. 93. Fluctuation in the Price of Eggs in the United
States as Compared with the Average of the Monthly
Figures for the Preceding Four Years
•The Government Crop Reporter is intended to be of service to farmers.
Any charts included should be as clear as it is possible to make them.
The illustration above is submitted only as a suggestion
Fig.
vertical scale, instead of being shown with 100 per cent to represent
unity, has zero placed opposite the line representing unity. The chart
does not clearly point out that the curve drawn above the zero or
unity line represents increases in revenues and not total revenues.
A much greater fault with the chart, however, is found in the fact
that the chart compares the operation of a railroad in different years
by using the year 1908 as unity. 1908 was a panic year, with very
serious business depression affecting railroads even more than some
102
GRAPHIC METHODS
1908
1909
1310
1911
38.93
7.ZZ
prosperity of the coun-
try were great enough,
it might even be pos-
sible to show in Fig. 94
a large increase in oper-
ating revenue due only
Annual Report of the Wheeling and Late Erie Railroad. 1918 tO the 'general imprOVe-
Fig. 94. Improvement in Economy of Operation of ment in business con-
the Wheeling ;and Lake Erie Railroad, 1008 (to 1912 ditions and ^ ^ of
It will be noticed from the upper left-hand corner of the chart that
the year 1908 is taken as unity. 1908 was a year of great business reduced efficiency
19/2
of the industrial companies. All the years following 1908 are likely
to show a greatly increased volume of business in practically any field
of commerce or industry. Because 1908 was selected as unity in Fig.
94, the reader would be justified in feeling that the increased amount
of revenue in the years
following 1908 might
have come solely from
the improvement in
general business condi-
tions, without any as-
sistance whatever from
ability in managing the
railroad. If the better-
ment in the general
depression. As business conditions naturally improved in the , , j.* £
years following 1908, there could be a legitimate question in the tne Operation OI
reader's mind whether the better showing of the railroad is due to • j- •J..,,! ^l^orl
better management or to the increase in the general prosperity ' LU
of the country sidered er se. It
in
s
per se.
not intended here to cast any reflections upon the managing ability
on the railroad in question. The only object in mentioning the matter
at all is to point out the fact that the use of the year 1908 as unity
puts the road unnecessarily under suspicion of attempting to mislead
the public.
In any chart where index numbers are used the greatest care
should be taken to select as unity a set of conditions thoroughly typical
and representative. It is frequently best to take as unity the average
of a series of years immediately preceding the years for which a study
is to be made. The series of years averaged to represent unity should,
if possible, be so selected that they will include one full cycle or wave
of fluctuation. If one complete cycle involves too many years, then
CURVE PLOTTING
103
the years selected as unity should be taken in equal number on either
side of a year which represents most nearly the normal condition.
Fig. 95 is an illustration reduced in size from a large chart 10 by 14
inches. The chart is of especial interest because it is one of a series
of several hundred charts submitted to the board of arbitration in
the concerted wage movement in the eastern territory by the Order
of Railroad Conductors and Brotherhood of Railroad Trainmen in
1913. These charts cover practically all phases of railroad operation
and give in condensed form a tremendous quantity of information.
RELATIVE RETAIL PRICES OF FOOD: SIMPLE AND WEIGHTED AVERAGES-UNITED STATES
1890-1912
AVERAGE PRICE FOR I89O-I8S9— IOO.O
Courtesy of F. J. Warne, Washington, D. C-
Fig. 95. Relative Retail Prices of Fifteen Principal Articles of Food in the United
States, 1890 to 1912, by Simple Averages and by Weighted Averages. Average
Prices for the Years 1890 to 1899, Inclusive, Were Taken as 100 Per Cent
The solid line shows ordinary averages of the prices for each year considered. In order to get the data for
the dotted line, estimates were carefully made of the average consumption in workingmen's families
of each of the fifteen various articles of food. The food prices were then "weighted" in proportion to
the quantities of each kind actually consumed and the averages shown by the dotted line were obtained.
The prices of foods to the workmen did not increase as much as the simple averages shown by the solid
line would indicate
There is such a great quantity of data arranged in convenient form
for reference, it seems likely that a person wishing to study railroad
operation could obtain more insight into present-day railroad condi-
tions by two-hours' study of this series of charts than he could pos-
104
GRAPHIC METHODS
gNOl dO SNOmiW
CURVE PLOTTING 105
sibly obtain by two months of reading the reports of transportation
companies and the pages of railway journals, and of asking questions
from railroad executives.
A heavy line in Fig. 95 shows the relative average prices of fifteen
articles of food used in workmen's families. Since the fifteen articles
of food are not consumed in equal quantities, or in equal value, it was
necessary to take into account the actual quantity or value used of
each kind of food. This was done by the method usually designated
by the name "weighted averages". It is obviously of less importance
to the workingman if the price of salt should increase 500 per cent
than if the price of bread or meat should increase 50 per cent. When
the fifteen articles of food are considered by simple averages, all foods
are considered as though used in equal quantities and a very great
increase in the value of some one food would seriously affect the simple
average even though that food is consumed in only small quantity.
By weighted averages the actual price of any food is multiplied by
the budget percentage figure showing the percentage of that food
used. The products resulting from the multiplication are added for
each year, and the totals or averages are compared on a percentage
basis to give a corrected comparison by weighted averages of food
prices in different years. The weighted averages represent more
accurately than simple averages the increases in food prices as they
really affect the pocketbook of the workingman. It will be seen at
the right of Fig. 95 that the heavy line for simple averages is consider-
ably higher than the dotted line representing the weighted averages.
This shows the amount of error which would have resulted in this
particular study if only simple averages had been used for comparison
instead of weighted averages. Weighted averages are of very great
importance in most studies relating to the cost of living, and they
could be used in other work much more widely than at present if their
importance and utility were more generally understood. It is un-
fortunate that in Fig. 95 the term "relative prices" is used in the
lower portion of the chart as the key for the dotted line. The simple
averages show relative prices also and the term "relative prices"
means practically nothing. The dotted line could more properly be
referred to by the term "weighted averages" as used in the title at
the top of the chart.
Fig. 96 is an example of a type of chart which can be of great
assistance to the chief executive of any corporation having a business
106 GRAPHIC METHODS
seriously affected by the ups and downs in financial conditions af-
fecting the country as a whole. In this chart, a study has been made
of supply and demand in the hope of getting some basis for prediction
in regard to periods of financial depression. The various factors
which might affect prosperity in steel construction \vork are assembled
here on one chart so that the whole situation may be studied con-
veniently and thoroughly. In a chart of this kind some estimates
and approximations must be made because it is usually impossible
to obtain accurate data to the extent desired. For work of this nature
it will ordinarily be found that a little "horse-sense", used in making
estimates for missing data, will permit the construction of a chart
giving an astonishingly large number of suggestions useful in deter-
mining the policy of a business, so that expansion and contraction
may be in harmony with the basic financial conditions of the country.
CHAPTER VII
COMPARISON OF CURVES
THERE are many men who from long experience have become
so skillful that they can glance down a column of figures and
obtain quickly a good idea as to the high points and the low
points shown by the figures taken as a whole. When it comes to
considering two or three columns of figures simultaneously to see
whether there is a similarity in the fluctuations shown by the various
sets of figures, the number of men who can intelligently grasp the
facts presented are rather few. It is in just such problems as these;
where a number of different sets of data must be compared, that curves
have tremendous advantage over presentation by columns of figures.
A man must be almost a genius to grasp quickly the facts contained
in several parallel columns of figures, yet anyone of average intelligence
can interpret correctly a chart which has been properly made for the
presentation of curves. Though there are numerous convenient meth-
ods which are useful in comparing curves, we can take up here only
the few of those which are likely to be of most frequent use to the
average reader.
Fig. 97 brings out the facts of its subject matter with splendid
clearness. There are relatively few men who could interpret quickly
the data for this chart, if the data were shown to them only as two
separate columns of figures. When a chart like that shown in Fig. 97
is used, no mental effort is required to get at the gist of the matter,
and the facts can be obtained much more rapidly than would ever
be possible by observing columns of figures alone.
A chart like that used in Fig. 97 can be prepared from tabulated
figures by any ordinary draftsman in less than one hour of work.
The cost of making a line cut is probably no more than the cost
of setting the type if the data are to be shown by tabulated fig-
ures. The space required for a chart like Fig. 97 is very little
107
108
GRAPHIC METHODS
£000
IgOOO
23496789 IO II 12 I 23456789 IO II 1
A_M. P.M.
Data of the New York Edison Company
more than would be required for the tabulated figures, and if there
is any serious limitation on space, Fig. 97 could be much re-
duced in size without detracting from its clearness.
Health-department
reports are not usu-
ally of interest to the
layman. Yet health-
department reports,
well presented, may
be of as much popular
interest as a well-
written magazine ar-
ticle. Fig. 98 is taken
from a commendable
report by the health
department of the
city of Boston. In
Fig. 97. Number of Telephone Messages Each Hour tne rePort itself, dif-
for One Day in a Business District in New York City ferent colors of ink
as Compared with a Residence District were used for the
Solid line, the "Broad" exchange — a typical business exchange . . ,
Dotted line, the "Riverside" exchange — a typical residence exchange VariOUS CUrVCS, With
Note the great number of business calls after mail has been opened in .-i re • e i
the morning and after return from lunch. In the residence district ^n^ CHCC I L empna-
there is much morning shopping by telephone sizing? the Contrast
Though the colored inks assisted in catching the eye of the reader,
the chart with curves designated by letters is usually sufficient for
all practical purposes whenever the curves do not cross overreach
other in such manner as to be confusing. As mentioned elsewhere,
a certain slope of a curve plotted on rectangular co-ordinate paper
does not in itself indicate a greater or less amount of increase or de-
crease than holds true for some other curve having a different slope.
The slope of a curve plotted on paper with ordinary co-ordinate ruling
depends largely on whether the data of the curve are in large figures,
so as to bring the curve near the top of the chart, or in small figures,
bringing the curve near the bottom of the chart. In Fig. 98 the fact
that curve A slopes more than curve C is due to the fact that curve A
is placed higher on the vertical scale of the chart than curve C. A
little study will show that the reduction in mortality portrayed by
curve A is much less -on a percentage basis than that depicted by
-surve C, yet curve A has the steeper slope. The slope of these two
COMPARISON OF CURVES
109
curves can best be compared if a pencil line is drawn in such manner
that the peaks above the pencil line are approximately equal to the
valleys below the pencil line for each curve.
Fig. 99 contains some interesting information. Though the chart
proves fairly well the close dependence of the price of cast-iron pipe
upon the price of the pig iron from which it is made, the chart is never-
theless misleading in that the first glance would indicate a much
greater fluctuation in the price of pig iron than actually occurred.
From the 1910 Annual Report of the Health, Department, City of Boston
Fig. 98. Deaths in Boston of Children under Five Years of
Age, under One Year, and from Five of the Principal
Infectious Diseases, Expressed as a Percentage of the
Total Mortality
Curve A. Deaths of children under five years of age as a percentage of
the total mortality
Curve B. Deaths of children under one year as a percentage of the total
mortality
Curve C. Deaths from Diphtheria, Scarlet Fever, Measles, Typhoid Fever
and Smallpox as a percentage of the total mortality
Note that Curve A shows a much steeper slope than Curve C, yet Curve C
drops in 1910 to less than half the figure for 1871. Curves plotted by
rectangular co-ordinates should not be compared by the slope of the
different curve lines
The reader is apt to overlook the fact that the vertical scale of the
chart does not extend below $11 per ton. He is quite likely to
think that the price of pig iron had all the rapid fluctuations which
would be indicated by the changing vertical distances between the
pig-iron curve and the bottom line of the chart itself. The amount
of fluctuation would look much less if the chart extended to the zero
line of the vertical scale.
110
GRAPHIC METHODS
There is probably a fallacy
in Fig. 100 because of the rise
in the general standard of liv-
ing between 1901 and 1906. It
is not fair to the 1901 Princeton
men to expect that they would
earn as much immediately after
graduation as men who gradu-
ated in a period of time several
years later. In addition to this
there is probably another serious
fallacy which affects all three
curves shown on the chart. The
income figures from which the
curves are plotted may not all
be shown on the same basis.
Men working on a salary have
as net cash all the money they
receive. Men in professions such
as law, medicine, etc., where
office rent and other expenses
are likely to be very heavy,
may report, as earnings, the
total amount of money received
without making corrections for
the expenses of conducting their
business. In other words, they
may very possibly in this case re-
port gross income instead of net
income. Such procedure might
tend to make the curves for
average income considerably
higher than they would other-
wise be.
Complex charts made up of
groups of bars as seen in Fig.
101 are much more common
than they should be. This type
of chart is very annoying to
COMPARISON OF CURVES
111
read because it is difficult for the eye to follow, through the whole
series, the bars representing any one set of facts which may be of
special interest. The bar method is in itself a simple one, but
when the bars are combined in the manner shown in Fig. 101 the
presentation becomes really more complex than if the data were shown
in the form of curves.
Fig. 102 certainly brings out the information of Fig. 101 in much
better form than any in which it is possible to show it by any com-
bination of bars either vertical or horizontal. The person who is
just beginning to chart data D°L5L0A£sr_
which he has used formerly
in tabulated form is often 2000
surprised to find how many .
inconsistencies exist in the
data and how many different
V IOOO
things there are which must
be allowed for by some 500
method of estimate. In Fig.
102 the data for the United °
Kingdom are expressed in
net tons, and for the United pigt I00. Comparison of the Earnings for Five
States in gross tons. Though Years after Graduation of the Yale University
some correction of the forms Academic Department Class of 1906, the
Yale Sheffield Scientific School Class of 1906,
of the curves as they appear and the Princeton University Class of 1901
in this chart WOuld of There is a fallacy in making this comparison. The standard of
living undoubtedly went up between 1901 and 1906
course have to be made to
get a true comparison of the shipping of the two countries, for our
purpose the thing of greatest interest is the general tendency of ship-
ping in the two countries. This we can study fairly well from the
general shape of the different curves, even though the curves cannot
strictly be compared with each other in so far as total quantities are
concerned.
Fig. 103 shows a convenient method for determining what fluctua-
tions in the different months of the year are typical for any subject
being studied. Instead of plotting one continuous curve by months
for a long series of years to a rather small horizontal scale, a large
horizontal scale is used and a separate curve is drawn for each year.
The curves for different years are placed one above the other, so that
any fluctuations which appear in the same months year after year
Yale.
Class'O6.
_. Sheffield. Princeton.
Class %O6. Class 'OJ
112
GRAPHIC METHODS
Tonnage engaged in DomesticTrade
Amounts in thousands of tons
will be apparent from the similarity in the shape of the curves for
the different years.
In order to use a fairly large vertical scale so as to make the fluc-
tuations stand out clearly, it was necessary to avoid entirely the
zero lines for the curves plotted in Fig. 103. The omission of the zero
Tonnage engaged in Foreign Trade lines may cause the fluctuations
from month to month to appear
greater than their true size would
warrant. It is sometimes possible
Gross lormaqe given for United States to plot a chart On the general
Net tonnage givenfbr United Kingdom Scheme of Fig. 103 SO as to USC Zero
lines, but many times it will be
found that the zero lines cannot
be used without adding confusion.
Though it would be preferable to
have the zero lines included, the
gain due to the arrangement of
the curves as shown here for
comparative purposes is great
O
O
o>
O
<T>
00
O
oo
CO
Si
I
•
f^
OO
3
HB
O
OO
enough to offset the disadvantage
of not having the zero lines on the
chart.
The zinc plate for Fig. 103 was
prepared directly from typewritten
copy, with no handwork involved
except to make heavier some of
the green background lines and to
draw the actual curves themselves.
Fig. 101. Comparison since 1850 of the Xr 4-- • TT<- i no 4.1, 4. *i, ii~
Merchant Tonnage of the United Notlce m Flg- 103 that the month
Kingdom with that of the United at the left of the chart is December,
States. Gross Tonnage is Given for and that the int plotted in each
the United States and Net Tonnage .
for the United Kingdom case lor December at the left is ex-
The chart is arranged backwards in that it reads actly the Same as the point plotted
from right to left. At first sight one thinks « xi TV i i
everything is growing smaller instead of larger. fOT the December SllOWn at the
The different bars sq^ closely grouped together ^^Vit of
Philadelphia Commercial Museum
o- oiir\7P>
are exceedingly difficult to interpret. See g < LFVe-
Fie- 102 repeating the last month of each
curve in this manner, the interpretation of the curves is much sim-
plified so that the reader can see at once what has been the tendency
of the curve from December to January each year. If the December
COMPAEISON OF CURVES
113
point were not represented at the left, it would be necessary for the
reader to glance several times from the left-hand end of one curve
to the right-hand end of the preceding curve to determine in his own
mind just what changes had occurred from December to January
185O
I860
1870
1880
1890
1900
Fig. 1 02. Comparison since 1850 of the Merchant Ton-
nage of the United Kingdom with that of the United
States
Gross tonnage is given for the United States and net tonnage for the
United Kingdom. Solid lines United States, dotted lines United
Kingdom. The "total" figures are not strictly comparable because
of the difference in registration method. The general tendencies
of the curves are instructive, however. Note the reduction in the
foreign trade of United States since the Civil War and the steadily
increasing foreign trade of the United Kingdom
at the end of each year. The repetition of the point for the last month
in each year saves time to the reader and also insures against errors
which might otherwise occur in the interpretation of the chart.
In Fig. 104 three distinct subjects are compared on one chart
and, at the same time, the data for each subject are shown for three
114
GRAPHIC METHODS
1906
1907
1908
1909
o
1910
1911
1912
1915
1914
O
4.4
4.0
3.6
4.4
4.0
3.6
4.4
4.0
3.6
4.4
4.0
3.6
4.4
4.0
3.6
4.4
4.0
3.6
4.4
4.0
3.6
4.4
4.0
3.6
4.4
4.0
3.6
MOHTHI.Y AVERAGES OP BUTTER FAT PT PTDIABAPOLIS MILK.
1906
1907
1908
1909
1910
1911
1912
1913
1914
Dec. Jan. Feb. Liar. Apr. May June July Aug. Sept. Oct. Hov. Dec.
Data of J. J. Hinman, Jr., Indianapolis Department of Public Health
Fig. 103. Monthly Averages of Butterfat Contained in Milk on the Indianapolis
Market, 1906 to 1913. The Curves Represent Averages from Several Hundred
Samples each Month
In order to find what fluctuations are typical for various months of the year, it is convenient to chart the
data as seen here with curves for different years one above the other. Definite peaks in April and in
October or November are seen at once. This chart is drawn on the same universal co-ordinate paper
shown also in Fig. 57, Fig. 130, Fig. 134 and Fig. 156
COMPARISON OF CURVES
115
JAN FEB MAR APR MAY JUNE JULY AUG SEPT OCT NOV DEC.
&I300
ZOO
'00
1000
900
800
700
600
500
400
300
200
100
--•^
I9IQ--
OPERATiNG R
OPERATI
NET OPERATING
EVEN JES
EXPENSES
1911
REX
ENUE
1912
Comparative Monthly Earnings and Expenses Per Mile cf Road
Frank Hatgh Dixon, in the Railway Age Gazette
Fig. 104. Comparative Monthly Earnings and Expenses per Mile of Road of Steam
Railroads in the United States Having Annual Operating Revenues of $1,000,000
or More
It is frequently convenient to superimpose curves for successive years, so that seasonal similarities and definite
increases or decreases may be accurately studied. Compare this chart with Fig. 103 and also with Fig.
204. It would be better if the heavy line border around the edge of this chart were omitted. The
heavy line at the bottom does not coincide with the zero line and the reader may be misled by reading
the chart from the border line
different years so that comparisons between these different years are
easily made. This scheme of superimposing curves for different years
is a very common one that frequently gives an arrangement more
convenient than could otherwise be obtained. It will be noticed
116
GRAPHIC METHODS
1900
1300
1700
1600
1500
1400
1300
1200
1100
1000
e
a 900
£
a
|800
3
700
600
GOO
400
300
200
100
Comparison of Electrical Output and Coal Consumption for Dec. 1912
and Dec. 1911, in Plant of Acker, Merrall & Condit Co. Building.
Dec.1911 34 56 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 1
Dec.1912 1 234 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
S S S C S
The Engineering Magazine
Fig. 105. Comparison of Daily Electrical Output and Daily Coal Consumption of a
Power Plant for the Same Month in Two Succeeding Years
There is a relatively small quantity of power needed on Sundays. In order to make possible a comparison
of the two curves for different years the horizontal scales for days were so placed that the Sundays would
coincide. With curves thus arranged,' the low points caused by Christmas do not fall on the same vertical
line, since Christmas is fixed by the day of the month instead of by the day of the week
COMPARISON OF CURVES
11,
in this chart that the December points have not been repeated at the
left and the reader is forced to glance between left and right in order
to make certain in his own mind just what changes occurred from
December to January each year. It can be seen that the January
figures for "Operating Revenues" are all considerably lower than
the December figures, but even so the reader has no clear idea of
the slope of the lines which would be most typical to portray the
changes from De-
cember to January
in each year. This
question of repeat-
ing one point for
curves of different
years superimposed
is referred to also in
Chapter XIII, Fig.
204.
Fig. 105, Fig. 106,
and Fig. 107 are self-
explanatory. They
show some interest-
Edwtn D. Dreyfus, in Industrial Engineering
Fig. 1 06. Average Temperature at Pittsburgh, Pa., for
Each Hour in the Day for Different Months hi the
Year. Plotted for Monthly Averages of Twenty-
Years Observations (1891-1910) of the United
States Weather Bureau
It would be impossible, using only columns of figures, to put this informa-
tion in such convenient form for reference and comparison. The
broad horizontal line at 10 degrees on the vertical scale of this chart
and of Fig. 107 is unfortunate since that line has no special significance
for persons reading the chart
ing applications of
curves to special
problems, and dem-
onstrate the great
convenience which
might result if curves
could be more generally used for presenting every-day facts to non-
technical readers.
In Fig. 108 we see the application of curves to the kind of data
of which it would be extremely difficult to give a clear understanding
if only columns of figures were available in the presentation. With
these two curves we are not so much interested in the total height
of the peak as in the general shape of the curve on either side of the
peak, showing whether there are any laws of uniformity in the increase
of the flood level and in the speed with which the flood subsided. The
two curves in Fig. 108 are quite different in their shape, although they
were taken for the same period of time in districts not widely sepa-
rated. The size and general character of different water-sheds have
118
GRAPHIC METHODS
a great effect on the nature of the floods which may result from any
definite rainfall.
In Fig. 109 also we are particularly interested in comparing the
shape of the curves for the distinctly different materials under con-
sideration. Here the curves represent reactions affected by the defi-
nite laws of physics, and we can join the plotted points resulting from
different observations so as to get smooth curves. Work in engineer-
ing, physics, and chemistry depends very largely on the interpre-
tation of smooth curves like these, and world progress would be
greatly retarded if the graphic method were not available to assist
in preserving and interpreting the results of elaborate experiment and
voluminous research.
In selecting a
scale for Fig. 110 the
draftsman is torn be-
tween a desire to
show the San Fran-
cisco fire peak at its
correct height, and
an opposing desire to
show on a large scale
the data for a whole
series of years so
that the fluctuations
from month to
month maybe clearly
defined. It seemed
best to cut off the
top of the San Fran-
cisco peak so as to
show the monthly
data on a scale large
enough to assure
clearness. To get the correct slope for the two sides of the San Fran-
cisco peak, a piece of paper was laid down adjoining the chart and a point
was located in the correct position for the top of the San Francisco
peak. The sides of the peak were then drawn so that they would
meet at that point if extended. Even though the figures for the San
Francisco peak are given at the top of the chart where the peak is
Edwin D. Dreyfus, in Industrial Engineering
Fig. 107. Mean Temperatures for Each Month in the Year
at Different Cities. Plotted from Records of the
United States Signal Service and of Blodgett's
Climatology of the United States
Information for eight different cities is so given that comparisons are
easily made. Note the different lines used here instead of colors.
Since Pittsburgh was the city under prime consideration, the Pitts-
burgh line was made heavy that it might be most clearly seen. This
chart gives a great amount of data in smaller space than would be
required to show the facts by any method othe" than the use of curves
COMPARISON OF CURVES
119
broken off, most readers will not imagine correctly the great height
to which that peak would extend if it were shown in full. The chart
could have been greatly improved if the upper portion of the peak
had been drawn in full size horizontally as though hinged near the
upper margin of the drawing. Since the full height of the peak is
30000
\ 25000
. 20000
10000
5000
24 25 26 27 28 29 30
March, 1913
10000
•30
8000
-¥
b>
t
§
?
to
u:
U
"ai 6000
<J 4000
200°
-10
25 26
27 28 29
March . 1913
-20
&
-/52
e
§
tf
-s
30 31
Engineering Record
Fig. 1 08. Comparison of Flood Rise in Two Rivers in New York State During the
Floods of March, 1913
In the preceding illustrations of this chapter there has been such similarity in the shape of the curves con-
sidered that they were superimposed for comparison. Here the curves are of different shape and they are
shown in separate fields so that the contrast may be more striking. The chart at the left should have
had the zero line shown. It is dangerous to base conclusions on the comparison of two curves unless
the zero lines are shown in each case
NICKEL STEELS
MANGANESE STEELS
3
160
140
140
100
r
?
N,
I
\
/
\
\
/
7
\
\
/
1 '
\
z
/
\
\
/
/
\
~
•"X
\
\
60
ii
\
/-
_^-
' ,'
\
s
I
z
^
\
/
SO
I 0
1
/
?
^
V
x
^
-S
V
a — -
^
**
CHROMIUM STEELS
8 1* 10 JO
4 8 18 16 30
L
i
A\
'1\
1
\
\
' 1
1
\
s
1
i
N
^~~,
• — — .
h
\
. —
—
1 —
/
\
^
•^
^
^--
^
^
^~- —
TUNGSTEN STEELS
4 ^ 1* IS 30 *» 88 32
/
v
\
5
^
^~^
/J
/
^x
_
/'
\
\
— .
—
~"
—
---
4 8 IS 16 •# 24 48 3
/row Age
Fig. 109. Comparison of Different Kinds of Steel Containing 0.2 per cent Carbon, as
shown by Tensile Tests on Specimens 100 mm. long and 13.8 mm. diameter. The
Vertical Scale Represents Thousands of Pounds per Square Inch and also Per-
centage of Contraction or Elongation
The heavy line shows ultimate strength
The dash line shows elastic limit
The dash-dot line shows percentage contraction
The light line shows percentage elongation
In this chart the thing of greatest interest is the contrast seen by comparing the shapes of the curves for
different steels. Though it is best to have curves of such distinct shape plotted in separate fields, i(
is ordinarily most convenient to have the fields themselves placed vertically instead of horizontally
420
GRAPHIC METHODS
COMPARISON OF CURVES
almost three times the height of the portion shown on this illustration,
it would be necessary to make two other hinges in the horizontal
extension so that the peak could be bent downward and turned back-
ward from right to left, giving something of a spiral effect. Though
this bent peak may seem rather artificial, it is quite certain that the
r
r
1(0 1
nn
18O1 1302 1903 1904 19O5 19O6 19O7 19O8 19O9 191O 191t
l_iJ New Building HM Fire Losses
NOTE- Values are given in Millions of Dollars
Adapted from Article by Roger W. Bat/son In the New York Times
Fig. in. Yearly Value of New Building Construction and Yearly Value of Buildings
Destroyed by Fire in the United States, 1901 to 1911, Inclusive
With this arrangement, the percentage value destroyed by fire can be seen more readily than from the
arrangement used in Fig. 110. The fluctuation from month to month cannot, however, be seen here.
If both charts are used, they supplement each other very well. Remember that for these two charts
the buildings destroyed are not necessarily the new buildings whose value is given. The black area
represents only the value of buildings destroyed whether new or old. Note the Ben Day shading
on the upper ends of the bars and the figures for the data from which the chart was made
GRAPHIC METHODS
30.40
30.30
tapering form of the horizontal extension of the peak would be under-
stood by even the untrained reader, much more certainly than the
chart as shown here with only the figures to indicate the full extent of the
loss which occurred in the San Francisco fire.
While Fig. 110
gives some general
idea of the propor-
tion which American
fire losses bear to
the value of new
building construc-
tion, the two fluctu-
ating curves make it
difficult for the reader
to make an estimate
of the percentage
losses year by year.
Fig. Ill supplements
Fig. 110, and gives
for each year the
total values for new
building construction
and the total values
of buildings de-
stroyed by fire. Here
the percentages of
the fire loss are quite obvious when judged by the extent to
which the black ink covers the shaded bar representing new build-
ing construction. Figures are given in each case for the reader
who may care to work out the actual percentage ratios. It must
not be assumed from the titles of Fig. 110 and Fig. Ill that the
buildings destroyed by fire are the same buildings whose value is re-
corded in the charts as "new building construction." The rapid
advance in the use of fireproof materials makes it likely that the fire
losses were more largely from older buildings, built by methods which
gave a structure less fireproof than the average for buildings put up
in recent years
Fig. 114 shows an error in curve plotting into which it is very
easy for an inexperienced person to slip. One vertical scale is relatively
S.OO 5.30 C.OO 6.30 7.00 7.30 8.00 8.30 9.00
P M Time Monday .March 14. 1910 P. M.
Sam. L. Naphtaly, in Journal American Society of Mechanical Engineers
Fig. 112. Record of Test of a Steam Turbine of 10,000
Kw. Normal Rating at Plant of City Electric Com-
pany, San Francisco, California
The different curves shown in this chart supplement each other so as
to give all the data on one chart in compact form. The scale for
each curve given at the left is only sufficient to show the maximum
and minimum value for each curve. The zero lines have been
omitted entirely. Though charts of this type with numerous curves
are sometimes desirable, they must be carefully made or the reader
will be misled by the fluctuations of some one curve appearing more
prominently than the data would justify
COMPARISON OF CURVES
123
larger than the other, and on that account the curves have been
made to coincide more closely than they would have done if both
scales had the same zero line. In making comparisons of this kind
care must be used to have the two scales start from the same zero
line, or the person presenting the charts will be open to the unpleasant
suspicion of attempting to "fake."
If the reader cares to see how these two curves would contrast if
properly plotted, the left-hand scale for "corn yield" can be changed
so that the different horizontal lines will be represented by the figures
0, 7, 14, 21, 28, etc. The data for "corn yield" can then be plotted
to the new scale, and it will be found that the new curve does not
coincide with the "rainfall" curve as closely as does the "corn-
yield" curve shown in Fig. 114. Though there is some similarity in
the shape of curves correctly plotted from these data, the similarity
is not nearly so exact as Fig. 114 would indicate.
Courtesy of System
Fig. 113. Records of Freight-Train Operation on a Large Eastern Railroad
Here, as in Fig. 112, the lero lines are not given and the reader must watch the left-hand scales carefully
to study percentage fluctuation. Comparison between curves cannot be made accurately by judging
from the slope or from the total fluctuation of the curves on the page. Percentage increases or decreases
for one curve compared with percentage increases or decreases of other curves give the best basis for
comparison
Curves well made ordinarily need no embellishment. Anything used for an eyecatcher should apply definite-
ly to the subject matter of the curves. Here the subject is freight-train operation, but the picture shows
the interior of a passenger train
GRAPHIC METHODS
Fig. 115 gives a good example of a total curve made by adding the
figures for different curves. Instead of using addition to get a set
of figures from which a total curve may be plotted, it is easier in most
cases to get the location of the total curve by the graphic method.
All that is necessary is to lay off, with draftsman's dividers, successively
on each vertical line, the height above zero at which each of the dif-
ferent curves intersects that vertical line. The totaling curve is
drawn through the points thus found. When there are not too many
curves, this method answers admirably. It sometimes happens that
actual observations for the data of different curves are not simul-
taneously taken and, for this reason, it may be impossible to add
the actual numerical data so as to plot a total curve. In such cases,
the graphic method
of stepping off the
height for the total
curve is practically
the only one avail-
able. After each of
the separate curves
has been plotted
from such data as
may exist, it is a very
simple matter by the
graphic method to
locate the total curve
from the separate
curves. A sufficient
number of vertical
lines are used to
bring the points on
the total curve close
enough together to
represent fairly the
data of the separate
curves which are
totaled.
In plotting curves relating to prices, it frequently happens that
there is a necessity for showing in the chart both the upper and lower
limits to which the prices may fluctuate in any given period of time.
\z ^
90 '91 '3E '93 194 55 "96 '97 '98 '99 '00 '01 OE
Adapted from Pennsylvania Farmer
Fig. 114. Chart to Show the Dependence of Corn Yield
upon the Quantity of Rainfall during the Month of
July. The Yield of Corn is Given hi Bushels per Acre
This chart is misleading. The close similarity of the two curves has
been obtained by plotting one curve on a larger scale than that used
for the other curve. The rainfall curve has been plotted with the
bottom of the chart as zero. The corn-yield curve is, however, drawn
with the scale starting at twelve.
COMPARISON OF CURVES
125
A -Hotel
B - Apartment House
C- Department Store
D- Combined Load Curve
E- Loft Building
F- Office Building
Note- Combined Load Curve
shown. Ln true size
Fig. 115. Typical Curves Showing the Twenty-Four Hour Demand for Electricity
during the Summer Months hi Various Types of Buildings in New York City
Curve D shows the fluctuations in the load on a power house supplying all of the buildings represented by
curves A, B, C, E and F. By combining loads of different types, the power plant can be kept more con-
tinuously busy than otherwise possible. After the other curves are all plotted, curve D can easily be
located by stepping off with draftsmen's dividers on each vertical line the heights of all the different
curves at that particular line
This is especially true where curves are plotted showing the fluctuations
in the market prices of stocks or bonds. In such cases, it is desirable
to plot two curves, one showing the minimum prices and the other
showing the maximum prices. When the two curves lie quite closely
together, it frequently assists in the clearness of the chart if the co-
ordinate lines are erased between the two adjacent curves. The erasing
of the co-ordinate lines makes the curves stand out much more dis-
tinctly than they otherwise would.
Charts on the general type of Fig. 116 are valuable to give a vivid
comparison. A chart of this kind would be especially striking if used
in advertising, or in a report where concentration upon only one gen-
eral idea was needed, without a great amount of specific detail. Though
Fig. 116 shows that telephone rates have had a constantly downward
126
GRAPHIC METHODS
trend as the number of telephones in use has increased, there is,
after all, no real proof in the chart that the rates have decreased
in proportion to the increase in the number of telephones in use.
Fig. 116 stimulates interest and makes one wish to plot another
chart in which the
number of telephones
in use would be the
horizontal scale and
the average rate paid
would be the vertical
scale, somewhat on
the general scheme
of Fig. 119. The
plotted points for
different years on a
chart of the kind
suggested would
in n
2,0
240.000
220.000
200,000
180,000 •
60,000 (O
140,000 g
20.000 ^
loo.ooo y
80,000
60,000
'0.000
20,000
Courtesy of Data, Chicago
Fig. 116. Chicago Telephone Rates per Year Compared
with the Number of Telephones in Use in Chicago
It is the object in this chart to show that the rates have been consistently
reduced as the number of telephones has increased. The curves
shown earlier in this chapter have varied directly, usually going up
or down simultaneously. Here we have an inverse relation, with one
curve coming down as the other goes up
show by the arrange-
ment of the points whether the prices had changed exactly in accord-
ance with the number of telephones in use.
Fig. 117 has been very carelessly drawn in that the two curves
do not have their vertical scales start at the same zero line. The
zeros for each of these scales are so close to the curves as drawn that
it would have been a very simple matter to have made one zero line
for both scales at the bottom line of the chart itself. The adverse
criticisms of Fig. 114 may be applied to this chart also.
Though the two curves in Fig. 117 seem to show some inverse
relation, since one curve frequently goes up when the other curve comes
down, the chart does not permit any measurement by which the degree
of correlation can be determined. The student who wishes to experi-
ment with this interesting set of data would do well to make an en-
tirely new chart with the two curves plotted from one zero line. After
this first chart has been made, a second chart can be drawn in which
the "Price" curve would be plotted exactly as in the first chart. The
curve for the number of barrels of "Exports" should, however, be plot-
ted downward from the top of the chart, after a good position has been
selected for the top of the chart so that the "Exports" curve plotted
downward from the top would coincide as nearly as possible with the
"Price" curve plotted upward from the bottom. The scales for the
COMPARISON OF CURVES
127
curves in the second chart should be the same as those for the first
chart, so that there may be no "faking" in any similarity which
may show up in the shapes of the two curves. It frequently happens
that the relations between two curves are such that the most striking
presentation can be obtained by plotting one curve upside down so
as to bring the two curves as closely into coincidence as possible,
and the scheme should be kept in mind as it is frequently of assistance
in making facts stand out vividly.
Courtesy of Pennsylvania Farmer
Fig. 117. Exports of Apples from the United States as Compared with the Average
Wholesale Price in the United States
A little inspection shows that the export curve usually goes up when the price curve comes down. Though
this fact indicates an inverse relation between the two curves under consideration it does not give
satisfactory proof that exports fluctuate relatively as much as price.
This chart is likely to mislead the reader because the two vertical scales do not have the same zero line.
Curves compared in this manner without having a common zero line should always be distrusted
Another interesting study can be made from Fig. 117 by drawing
a chart with "Price" as the horizontal scale and quantity of "Exports"
as the vertical scale. Dots for the different years placed on such a
chart, after the general manner of Fig. 119, will appear so widely
scattered over the whole field that the reader will find it almost hope-
less to draw any general conclusion from the arrangement of the
dots. Though the dots indicate by their position a general tendency
128
GRAPHIC METHODS
for exports to decrease as prices increase, there would seem to be
so many complex factors entering into the relation that no very gen-
eral law of dependence can be proved.
It can be seen from inspection that the relations existing between
the two curves of Fig. 118 are much closer than exist between the
two curves of Fig. 117. It is unfortunate that in Fig. 118, as well
as in Fig. 117, the chart was carelessly prepared so that the two curves
do not have the same zero line.
Courtesy of Pennsylvania Farmer
Fig. 1 1 8. The Average Price of Apples in the United States as Compared with the
Total Supply
Here again an inverse relation is indicated, but the chart has carelessly been made with the two vertical
scales starting from separate zero lines so as to cause, distrust by the reader. The chart is printed show-
ing a finely ruled co-ordinate background, though only every tenth line is desirable for the reader. The
use of more lines than necessary should be avoided as it tends to cause confusion. See Fig. 119 as
another method of charting the same data
In order to determine just how closely the price of apples depends
upon the supply, Fig. 119 was prepared from the data of Fig. 118.
Though the dots in Fig. 119 represent a rather long series of years,
they nevertheless have a fairly symmetrical arrangement and the
general tendency might, be approximated by a smooth curve drawn
as shown. It must be remembered that there are many conditions
which may affect the position of these dots on the chart. For one thing.
COMPARISON OF CURVES
129
Price per Bbl
*e oo
V50!,
«
\
•1904
the standard of living has very greatly changed in the period of time
from 1895 to 1912. Prices in recent years might be expected to be
considerably higher than in the earlier years, without any regard to
the size of the apple crop. Besides this, numerous diseases have
affected apple trees in recent years, requiring more care than formerly
to produce good fruit. This would also have some tendency to raise
prices in spite of the tremendous number of apple trees which have
come into bearing in the
later portion of the period
of time under consideration.
The general method of plot-
ting shown in Fig. 119 is
of great importance and it
should be kept in mind
whenever two curves are
found having similarities
such as are seen in Fig.
118. Other examples of this
o 5 ,o ,5 eo £5 =o 35 .o ,5 60 55 «-•-»-» method of plotting to study
Quantity /n Millions of Bb.§. the correlation of two related
Fig. no. The Average Price of Apples in" the u • -n u f j • 4.1,
United States as Compared with the Total subjects will be found in the
Supply last portion of Chapter X.
By this method, the positions of the dots on the chart show ' J^jo- 120 Contains much
whether there is any close relation between supply and ^ °"
price. The dots fall in fairly regular order, proving better information f Or the Student
than Fig. 118 that the price does largely depend upon the „ 1*4. TTT i
supply. A smooth curve has been drawn to represent OI JllStory. We are nere m-
approximately the general relation between supply and , frl-r»+' 11 ' +Vi
price which the dots might seem to indicate. Note that T Uiariy in IHC
the year is stated for each dot shown record of the United States.
That curve line has accordingly been made much heavier than any
of the others, so that it may be brought prominently to the eye of
the reader. By visually projecting the curves for Russia and the
United States beyond the limits of the chart, it appears that we should
equal Russia's population within the next few decades. It must be
remembered in viewing this chart that the populations of the Asiatic
countries (especially the populations of China and India) are not shown
here. If all the countries of the world were considered, it would be
seen at once that for many years to come there is no likelihood of the
United States having the greatest population in the world. It is only
because Asiatic countries have been omitted that we seem to be so
nearly the head of the list.
I8OO
no
18(0
1820
1830 I84O
I85O
105
too
95
90
85
60
75
™
65
I 6O
Z
55
50
0 45
35
30
25
20
15
10
I860 1870 1880 I89O I9OO
no
INCREASE OF POPULATION
IN THE
UNITED STATES
ANDTHE
PRINCIPAL COUNTRIES OF EUROPE
PROM
180OTOI9OO.
IOJ5
IOO
95
90
as
60
75
70 .f
Z
65^
60 r
Z
55
0
SO
U)
z
45 O
J
40 i
35
30
as
ao
15
10
5
ISOO 1810 1620 1630 |64O I65O ISfoO 1S7O I860 I09O I9OQ
From the United States Statistical Atlas, Census of 1900
Fig. 120. The Population of the United States Compared with the Population of
the Principal Countries of Europe from 1800 to 1900, Inclusive
Written words requiring one hour to read could not convey as much information as this chart gives.
In considering the slope of the curve for the United States it must be remembered that the slope of a
curve does not indicate the percentage rate of increase or decrease. The increasing slope of the United
States curve does not in itself prove any increase in the percentage rate of growth. Compare Fig. 121
130
COMPARISON OF CURVES
131
The reader should keep constantly in mind when viewing Fig. 120
that the slope of a curve line crossing a field ruled with ordinary rec-
tangular co-ordinate lines on an arithmetical scale tells nothing about
the percentage rate of growth from period to period. The slope of
the United States curve is very much steeper in the upper portion
of Fig. 120 than in the lower portion, but the greater slope does not
prove that we are growing more rapidly on a percentage basis than
early in the century. The slope of a curve plotted on a natural scale
of rectangular co-ordinates shows only the size of the increments added
from period to period and it tells nothing whatever about percentage
growth.
Fig. 121 has been drawn to
assist in proving the preceding
statement regarding curve slope.
Starting with one dollar, it was
assumed that a uniform increase
of 10 per cent of the accumu-
lated amount would be made at
the end of each year. This is the
same as though the dollar were
placed at 10 per cent compound
interest. At the end of thirty-six
years it can be seen that the one
dollar has increased to nearly
thirty-one dollars. Though the FiS' »z- ^f, Showing the Growth
of One Dollar at 10 per cent Com-
pound Interest for Thirty-six Years
Here the rate of increase is uniformly 10 per cent
per year, but the slope of the curve is constantly
changing. The general shape of this curve is
somewhat similar to the shape of the population
curve for the United States seen in Fig. 120.
The slope of a curve plotted on ordinary co-
ordinate paper tells nothing about the per-
centage rate of growth. See Fig. 122 and Fig.
123
accumulated fund is shown by a
smooth curve throughout the
period of thirty-six years, the curve
is constantly changing its slope in
spite of the fact that the rate of
increase remains constant at 10 per
cent per year. The curve in Fig.
121 is very similar in shape to the curve for the United States in Fig.
120. This similarity in shape shows conclusively how much the reader
would be misled if he should assume that the increasing slope of the
curve in Fig. 120 proved in itself an increase in the rate of growth.
The actual percentage rate of the growth for Fig. 120 can best be stud-
ied by making an entirely new chart for the purpose of observing
percentage rates only.
132 GRAPHIC METHODS
* The ordinary form of graphic chart plotted on rectangular co-
ordinate paper with the natural or arithmetical spacing of the lines
has some serious limitations which may cause a chart to be misleading.
The true function of such a chart is to portray comparative fluctua-
tions. This desired result is secured clearly and satisfactorily when
the factors or quantities compared are of nearly the same value or
volume, but analysis will show that the result is not accomplished
when the amounts compared differ greatly in value or volume. The
extent or degree of the fluctuation as indicated on the ordinary chart
depends in a measure on the proximity of the curves to the top or bot-
tom of the chart. The chart registers the actual change in the value
rather than the ratio or percentage of change. The wider the range
of scale the greater the variation between the actual and the relative
changes.
This same criticism applies to charts which employ two or more
scales for various records or curves. If the different scales are in
proper proportion the result is the same as with one scale, but when
two or more scales are used which are not proportional, an indication
which is absolutely false may be given with respect to comparative
fluctuation. Charts made on a percentage basis are used to some
extent in graphic work, and these correct the deficiency in the ordinary
chart by showing the changes in the percentages of increase or decrease.
In correcting one deficiency, however, another is introduced. The
percentage scale gives no clue to the magnitude of the quantities
represented by a curve. The true proportions of relative changes are
shown, but the actual values are not indicated. The use of the per-
centage scale also requires considerable labor for computing the per-
centages of change.
As a substitute for the ordinary (or natural) scale and for the scale
of percentages, as well as for compound scales, the logarithmic scale,
or scale of ratios, practically meets all the requirements. The logarith-
mic scale permits the exhibition of both actual and relative values
and actual and relative fluctuations. While some knowledge of log-
arithms will make plain certain features which otherwise are hard to
understand, no special knowledge of higher mathematics is essential
to the use of the logarithmic scale. The principles involved are the
same as those embodied in the slide rule, and any treatise on the slide
* Portions of this discussion on charts plotted by the logarithmic scale are adapted from an article by W. J. Cunningham,
in the Railway Age Gazette, June 25, 1909.
COMPARISON OF CURVES 133
rule will make them sufficiently clear. A person who can plot a chart
to the ordinary scale should have no difficulty in using the logarithmic
scale.
No matter what the location on the chart, if the logarithmic
spacing is used on the vertical scale, for curves, the angle of the upward
or downward inclination is the same for all curves affected by the
same percentage of change. Curves having an increase equaling
the distance from 100 to 200, 200 to 400, 300 to 600 (or the distance
between any number on the scale and double that number) have an
increase of 100 per cent and show the same slope. It will be noticed,
for instance, from any paper ruled logarithmically, or from Fig. 123,
that the distance on the logarithmic scale from 10 to 20 is the same
as from 200 to 400.
In Fig. 122, we have curves plotted for comparative study in the
manner most convenient when ordinary arithmetically ruled cross-
section paper is used. Some of these curves represent large quantities,
so that they are on the upper portion of the chart, while others rep-
resent comparatively small quantities and fall near the bottom of the
chart.
Just because the curves in the upper portion of the chart represent
numerically larger quantities, they have much more vertical movement
up and down on the face of the chart than those curves in the lower
portion of the chart which may have an even greater amount of per-
centage fluctuation. This wide difference in the amount of vertical
movement on a page is one unfortunate source of confusion to persons
who are just beginning to study curve charting.
Fig. 123 is plotted from the same data as Fig. 122, but it is on
paper having logarithmic spacing for the vertical scale with the ordi-
nary arithmetical spacing for the horizontal scale. With the logarith-
mic spacing on the vertical scale the fluctuations in the different
curves show in true proportion. Curve F appeared insignificant in
Fig. 122 because it happened to fall near the bottom of the chart
where percentage fluctuations are not prominently shown. In Fig.
123, however, curve F shows up as having far the greatest percentage
changes of any curve on the whole chart. For persons who under-
stand even slightly the principles involved in reading charts plotted
on logarithmic paper, Fig. 123 shows up the facts in much more con-
venient form than Fig. 122. To make comparison most convenient,
the two figures are placed on facing pages, 134 and 135.
134
GRAPHIC METHODS
1301
I90Z
1903
1904
W. J. Cunningham, in the Railway Age Gazette
Fig. 122. Passengers and Employees Killed and Injured
in Train Accidents for All Railroads in the United
States. (From Quarterly Reports of the Interstate
Commerce Commission)
Curve A. Passenger miles (2000 on scale equals 20 billion passenger
miles)
Curve B. Ton miles (2000 on scale equals 20 billion ton miles)
Curve C. Number of employees injured
Curve D. Number of passengers injured
Curve E. Number of employees killed
Curve F. Number of passengers killed
Compare this chart with Fig. 123. The data plotted here by the or-
dinary natural scale of co-ordinates are replotted in Fig. 123, using
logarithmic co-ordinates. Note the peak in 1904 in Curve D.
The number of passengers injured was approximately doubled in a
short period of time. In the same period of time the number of
passengers killed increased to seven times what it had been, yet the
peak on Curve F does not attract great attention. Notice these same
peaks in Fig. 123 with the logarithmic scale
It is unfortunate that there is so much difficulty in obtaining
paper having the logarithmic ruling in one direction and the arith-
metical ruling in the other direction. The arithmetical ruling in one
direction is essential for statistical work, since we must ordinarily
plot as one scale data representing years or other subdivisions of
time. In statistical work we cannot well use a paper having logarith-
mic ruling in both directions, yet that is the only kind of logarithmic
paper which can be obtained from most stores selling drawing materials
COMPARISON OF CURVES
135
1904
I90S
1305
I9O7
taog
I
W. J. Cunningham in Railway Age Gazette
Fig. 123. Passengers and Employees Killed and Injured
in Train Accidents for All Railroads in the United
States. (From Quarterly Reports of the Interstate
Commerce Commission)
Curve A.
miles)
Curve B.
Curve C.
Curve D.
Curve E.
Curve F.
Passenger miles (2000 on scale equals 20 billion passenger
Ton miles (2000 on scale equals 20 billion ton miles)
Number of employees injured
Number of passengers injured
Number of employees killed
Number of passengers killed
This illustration is a replot of Fig. 122 by using the logarithmic scale in
the vertical direction. In reading a chart .in which a logarithmic
vertical scale is used, attention may be given to the slope of the curve
lines. Curves having the same slope upwards or downwards have
the same percentage change. Note that curves with a logarithmic
scale do not have zero for the bottom line of the chart. It is, how-
ever, desirable to have the bottom line either at ten or some power
of ten on the vertical scale
and engineering supplies. A person doing statistical work for which
paper with the logarithmic ruling is desirable may occasionally have to
rule his own paper. This, however, is not an impossible task especially
if one has a slide rule. The spacing of the lines can be copied from
either scale of the slide rule, or it may be worked out easily to fit any
136
GRAPHIC METHODS
given space by dividing into tenths and hundredths and using tables
of logarithms.
It is of interest to note here that the data of Fig. 121 would show
as a perfectly straight line if plotted on paper having the logarithmic
/uling for the vertical scale. Since the increase from year to year is
uniform, on a percentage basis, the points of the curve all fall on a
straight line drawn from the first point to the last point.
a
1,BOO.OOO
1
a
t
i
i
i
c
I
7
\
0
s
1
1
'
i
3
[
1
)
1
j (
1
6
1
a
I
I
1
1
I
\
|
1
I
9
1
0
2
'l
i
i
i
i
-T
T71
TT
^-
"T5(
fin
FBI
V1
400.000
c
C
*=
^
-?
^
r-'l
S
2
K
fli'Y1
rr*i
fHl
f T
it
S
smn ooo
i--.
fnn nnn
/
\
.--
,'
',
ISO.OOO
>'
\
1
PIIH
1
>-"
j
il
"
!
|
7
>-^
\
100. OOO
i
'»
^
^>
fft nnr
m|
Tit
V
«
\
•-
An nnn
--^
---^
•xn nnn
9n non
TT. J. Cunningham in Proceedings of New England Railroad Club
Fig. 124. Book Value of Material on Hand for a Large Eastern Railroad
The logarithmic scale is particularly valuable for an operating chart such as this when there is a great differ-
ence in the size of the figures which must be compared. The lower curve here averages about $60.000
while the upper curve averages about $1,100,000. The logarithmic scale permits accurate comparison
of various curves to determine whether any curves are out of harmony with the other curves
Fig. 124 gives an especially interesting use of curves on the log-
arithmic ruling. Executives who have puzzled over methods for
controlling the quantity of materials or supplies on hand realize full
well that it is sometimes just as important to watch the curves for
materials having only a relatively small consumption as it is to watch
the curves for those materials of which the greatest quantity is used.
The mere fact that great amounts of capital are tied up in stocks
of certain largely used materials tends in itself to cause very careful
scrutiny of those accounts, while numerous small or inactive accounts
may be entirely overlooked or neglected. A little study often shows
that there is no necessity for carrying so much material on hand.
COMPARISON OF CURVES 137
If charts similar to Fig. 124 are used, the executive can tell instantly
whether the stocks in different departments or of different kinds of
material are increasing or decreasing simultaneously and propor-
tionately.
"To summarize — with the ordinary arithmetical scale, fluctuations
in large factors are very noticeable, while relatively greater fluctua-
tions in smaller factors are barely apparent. The logarithmic scale
permits the graphic representation of changes in every quantity with-
out respect to the magnitude of the quantity itself. At the same
time, the logarithmic scale shows the actual value by reference to the
numbers in the vertical scale. By indicating both absolute and rela-
tive values and changes, the logarithmic scale combines the advantages
of both the natural and the percentage scale without the disadvantages
of either."
CHAPTER VIII
COMPONENT PARTS SHOWN BY CURVES
IN Chapter I various examples were given in which the component
parts or factors making up a complex whole were shown in their
relative sizes. It frequently happens that it is necessary to
show the changes which occur in the size of different components
as time goes on. In this chapter we shall consider only examples
of charts showing the fluctuating size, at different times, of com-
ponents which make up a total of 100 per cent.
In Fig. 125 the
proportionate num-
ber, voltage, and
candle-power of
various types of
standard incandes-
cent lamps delivered
in different years by
the New York Edi-
son Co. are shown
in a series of vertical
bars which are all of
the same length,
representing 100 per
cent. No statement
is made or implied
in regard to the total
figures, which may
have increased or
decreased from year
to year. All we are
interested in, in this chart, is the proportion of the different components
which in their aggregate make up the bar representing 100 per cent
in any year.
In Fig. 126 the total height of the chart represents 100 per cent.
138
New York Edison Company
Fig. 125. The Number, Voltage, and Candle-Power of the
Different Types of Standard Incandescent Lamps
Delivered by the New York Edison Company in
Different Years, Shown as a Percentage of the Totals
of All Lamps Delivered
The chart was drawn in four contrasting colors and was framed for a
wall exhibit
COMPONENT PARTS SHOWN BY CURVES
139
Per Cerrt
U.S. Foreign
1OO O
1O
1820
183O
164O
1850
186O
187O
188O
1890
13OO
Fig. 126. Percentage of United States Foreign Trade Carried in American Vessels
and in Foreign Vessels by Decades, 1820 to 1900
This type of chart requires a more highly educated reader than the type of chart shown in Fig. 125, but it
gains by making the information stand out more clearly than possible with a series of bars
To show that the chart is absolutely limited to the height represent-
ing 100 per cent, we use a broad line for the zero line and another
broad line at the top for the 100 per cent line. Instead of showing
the percentages at different decades by the method of shaded bars
used in Fig. 125, the vertical lines representing decades are first marked
with points dividing the lines into component parts, then the points
on the various lines are joined to give a curve. The area under-
neath the curve is shaded in this illustration simply to give a great-
er contrast between the two portions of the chart. Charts of this
kind made with shaded or colored areas are understood by a sur-
prisingly large number of people who ordinarily would not under-
stand a chart made by using curve lines without the shaded or col-
ored areas.
The double scale at the right of Fig. 126 is worth noting. The
percentage for the United States can be read for any decade. The
percentage for foreign vessels can also be read for any decade by using
the reversed scale, in which zero is placed at the top and 100 per cent
at the bottom. Though a double scale is scarcely necessary on a
chart as simple as Fig. 126, it is frequently desirable to have a double
scale.
Another very striking wall chart is shown in Fig. 127. Here as
in Fig. 125 the chart was framed, but the frame shows in the photo-
graph only as a black border. In making up this chart co-ordinate
140
GRAPHIC METHODS
paper was used for a background. The upper half of the chart shows
the 24 hours of the day divided between hours of darkness, hours of
twilight and cloudiness, and hours of sunshine, totaling 100 per cent
for each month in the year. The hours of darkness are definitely
known from almanac figures and can be plotted as a smooth curve.
AN ABUNDANCE OF LIGHT TENDS TO
PREVENT INDUSTRIAL ACCIDENTS
New York Edison Company
Fig. 127. Industrial Accidents in Different Months
of the Year Compared with the Hours of Sun-
light Each Day in Different Months According
to Weather Records for New York City in 1910
Twenty-four hours in a day are shown as 100 per cent divided
between darkness, semi-darkness, and sunshine. Curves
showing accidents for three different years have the same
general shape as the upper curve representing hours of dark-
ness. The scale for the accident curves should have been
started so as to show zero at the bottom of the curve field
The hours of cloudy weather, however, vary in different years. The
area showing cloudiness and twilight was drawn from actual weather
observations made in New York City during the year 1910. The per-
centage of sunshine in different months fluctuates considerably, as
will be noticed in the chart.
COMPONENT PARTS SHOWN BY CURVES 141
The lower half of Fig. 127 contains three curves showing the
monthly distribution, for three successive years, of about 700 deaths
annually from industrial accidents reported from an area embracing
80,000 plants. The similarity of these curves, showing the number
of fatal accidents per month, to the curves showing the percentage of
darkness, is intended to convey to the person seeing the wall exhibit,
the truth of the statement at the top of the chart, that "an abundance
of light tends to prevent industrial accidents." Though Fig. 127 is
a very commendable and effective piece of work, it should be pointed
out that there is danger of exaggerating the facts in the way in which
the chart is prepared. The lower left-hand scale does not begin at
zero. By measuring, it can be seen that the scale begins at 20 acci-
dents per month. The bottom line of the curve field should have
been drawn near the edge of the picture frame to represent zero.
This change in the bottom line would have given the reader a more
accurate idea of the increase of deaths in those months having the
greatest proportion of darkness. This chart really does not exaggerate
the facts seriously, for the three curves for deaths and the curve for
darkness would really be of approximately the same shape even if
the zero line had been shown in its correct position. Yet it is a fact
that the omission of the full scale in the chart may cause a person
glancing hastily at the chart to -distrust it simply because the zero
line is not shown.
In Fig. 128 a number of different components are shown to make
up a total of 100 per cent. This type of chart is especially good to
give instantly a general idea of the relative size of the components
or factors which enter into any total, and to show the changes in these
factors as time goes on. Though it is fairly easy to see in Fig. 128
what the changes are which have occurred in, say, the item for "Gen-
eral" expenses, it is not at all easy to determine the changes which
have occurred in the item for "Conducting Transportation." The
eye cannot measure correctly the increase or decrease in width of any
area as great as that representing the item for "Conducting Trans-
portation," especially if there is no straight line to gauge by, either
at the top or the bottom of the area under consideration.
Though the method of presenting the facts in Fig. 128 is excellent
to give a rough general idea or to reach unskilled readers, the method
of presenting the facts in Fig. 129 is likely to give the more accurate
impression. In Fig. 129, each of the different expense accounts is
142
GRAPHIC METHODS
Percent
1OO
plotted as a separate curve measured from zero as a base line. It can
be seen at once in Fig. 129 that the component for "Conducting
Transportation" increased rapidly until 1895, ran along fairly uniformly
to 1900, then slightly decreased, then increased again. By having
each curve plotted separately with the points measured from a zero
base line, the eye can judge instantly and accurately the changes
which have occurred over a period of years in any component which
enters into the total. In an illustration like Fig. 129 it should be
shown in the title,
or preferably on the
chart itself, that the
sum of the heights
of all the curves
given on the chart is
constantly 100 per
cent as indicated by
the broad line at the
top of the chart.
The reader will then
know that if any one
curve on the chart
goes up, some other
curve or curves must
come down in order
that the 100 per cent
line may remain
straight and hori-
zontal.
Fig. 130 is an interesting application of the method of using areas
to show components with 100 per cent shown as a straight line at the
top of the combined area. As in this case a large part of the con-
struction work was finished, the actual number of accidents in the
construction department dropped to almost nothing, and, because
the shaded area for construction grew less, it was necessary that the
other areas should widen out if the 100 per cent line at the top were
to remain a straight line. Here the weak point in the method of
charting is the same as that indicated for Fig. 128. The person ob-
serving the chart has no way of telling whether the factors included
in the 100 per cent have grown less or grown greater, and whether
O — CM co sj- in
O ,O ,O jO .O -O
0)
O -
9
Adapted from Railway Age Gazette
Fig. 128. Percentage 'Distribution of the Expenses of
Operating the Railroads of the United States
Here a number of different factors enter into the total 100 per cent.
Since the strips representing different expenses vary at both top and
bottom, it is not easy to see from year to year how much any strip
may be increasing or decreasing. Compare with Fig. 129
COMPONENT PARTS SHOWN BY CURVES
143
the quantities represented by the different areas have changed in
actual size or only in relative size. Where great fluctuations occur
from time to time and many factors enter into the total, it is best
to draw charts in the form of Fig. 129 with a common zero line, or in
the form of Fig. 131, where each factor has its own separate base line,
or in the form of Fig. 132 and Fig. 133, in which the lines on the chart
represent actual quantities rather than percentages of an aggregate or
total sum.
Note in Fig. 130 and Fig. 131 the 8l/2-hich by 11-inch co-ordinate
paper on which the ruling is so arranged that the paper may be used
for almost any subdivisions of time, such as days, weeks, months,
etc., as seen in Figs. Percent
57,103. 131, 134, and
156.
In Fig. 130 the
paper was used for a
time-scale of three
years by months,
the total height of
the chart being put
at 100 per cent, us-
ing fifty out of the
fifty-two spaces on
the paper. Fifty-two
spaces, correspond-
ing to the number of
weeks in a year, of
course are necessary
when the paper is
used to
weeks
30
80
7O
60
50
^Conducting Transportation-^
Fig. 129. Percentage Distribution of the Expenses of
Operating the Railroads of the United States. The
Combined Height of All the Curves Shown Equals
100 Per Cent on the Scale
This illustration represents the same data as Fig. 128. Here the per-
centage for each expense is read from the zero base line instead of
.from one to the other of the fluctuating lines on either side of an
area. This method, though not so popular as the method of Fig. 128,
permits more accurate reading
represent
on the long
dimension of the
sheet.
Fig. 131 and Fig. 130 depict exactly the same data. In Fig. 131
the facts, which in Fig. 130 were represented by areas, are shown as
separate curves, each curve with its own base line. Having this series
of separate curves on one sheet of paper permits an executive to com-
pare the number of accidents in one department with the number
of accidents in any other department at any one time, or to study
144
GRAPHIC METHODS
O
Humber of accidents occurring in each department, as
PERCENTAGES OF THE TOTAL.
12 Months Averages.
Tterceni
8
0 I
Fig. 130. Percentage of Accidents Occurring in Each Department of a Large Industrial
Plant. Plotted Monthly by Twelve-month Averages
By this method, with a constant width to represent 100 per cent, any great change in any component
affects all other components. Here the decrease in construction accidents causes the areas depicting
other accidents to increase in width, even though there may be no increase in the actual number of
accidents. Compare Fig. 131
This cut was made from specially ruled co-ordinate paper 8j^j inches by 11 inches, with all lettering done by
typewriter. The ruling as used here shows 100 per cent and three years by months. Note also Figs. 57,
103, 134 and 156, for which this same universal ruling has been used
COMPONENT PARTS SHOWN BY CURVES
145
Num'ber.
ACTUAL IIUI.TBER OF ACCIDSIITS
occurring in each department (
12 Months. Averages.
Hunter.
1910-11
1911-12
1912-13
Fig. 131. Actual Number of Accidents Occurring in Each Department of a Large
Industrial Plant. Plotted Monthly by Twelve-month Averages
In this chart the actual condition in each department can be seen much more clearly than by the method
used in Fig. 130. Here each department is judged by its own record without danger of unjust criticism
based on conditions in other departments
For a moro complete discussion of Figs. 130 and 131 and of the contrast of methods followed in preparing
them thi- reader is referred to pages 142, 143 and 146
146
GRAPHIC METHODS
the fluctuations in the accidents of any one department over a long
period of time.
As accidents never occur with any regularity, curves representing
the actual number of accidents are likely to fluctuate a great deal.
There was such variation in the different months for the number of
accidents represented in Figs. 130 and 131 that it was almost im-
possible to draw any definite conclusion from curves for monthly
NATURE OF THE LOAD CONNECTED
TO THE SYSTEM OF THE
NEW YORK EDISON CO.
New York Edison Company
Fig. 132. Nature of the Electrical Load Connected to the System
of the New York Edison Company, 1893 to 1912
In the preceding illustrations 100 per cent was indicated by a straight line at the
top of the chart. Here the line representing 100 per cent is a curve. Though
the actual sizes of different components can be seen by this method, percentages
can only be estimated from the widths of the areas. The scale for this type of
chart must read in actual quantities rather than in percentages. On this wall
exhibit the scale has been omitted entirely
data. The data for Fig. 130 and for Fig. 131 were plotted on the
basis of giving, monthly, the average number of accidents in each
department during the last twelve months for which records were
available. Actual figures in tabulated form were used to show for
immediate reference the number of accidents in any month. The
curves on the twelve-months average basis were consulted to deter-
mine whether there was any great increase or decrease in any de-
partment.
In Fig. 132 the vertical scale was omitted, perhaps with the idea
that the chart would thus appear more simple to the average indi-
COMPONENT PARTS SHOWN BY CURVES
147
vidual attending a large exhibition. If the scale were given, however,
it would be plotted on the basis of actual horse-power rather than
on percentage, for the top curve here represents the total quantity.
Percentage scales cannot well be used in diagrams of component parts
if a fluctuating curve line instead of a horizontal line representing
100 per cent is given at the top. The reader may, however, get a
fair idea of the percentages if he roughly calculates the height of the
areas in question on any vertical line of the co-ordinate ruling and
then, using that vertical line as a measuring rod, estimates the height
of the areas as a percentage of the total height of the chart.
In Fig. 133 the straight line at the top of the chart does not have
any significance, as it is due only to the co-ordinate ruling which
serves as a background to the chart itself. The important part of the
chart ends at the top of the shaded area. We may consider the top
of the whole shaded area as a curve and read the values accordingly
from the scales on the right- and left-hand sides. In fact, any curve
on the whole chart may be considered as a sub-total, which includes
all of those components or factors shown as separate areas beneath
that curve. Thus the "Total Shop Cost" includes all those com-
ponents shown below the "Total Shop Cost" curve.
Jon
Apr
May
June
July
Aug Sept
Nov
Dec
Adapted from Factory
Fig. 133. Factors Entering into the Total Costs and Estimated Value of the Product
of a Manufacturing Plant
The various elements entering into total shop cost are plotted, each built up 0.1 the areas below. The
"Estimated Valuation" is based upon market prices for the finished goods. Vertical distances between
the "Total Cost" curve and the "Estimated Valuation" curve show the estimated profit. Note the
use of dimension lines in combination with the scales
148 GRAPHIC METHODS
The use of engineering dimension lines in Fig. 133 is of interest,
for the dimension lines add considerably to the clearness of the drawing.
In the center of the chart the vertical dimension lines on both sides
of the names for each area show distinctly that the chart must be
read on the basis of the vertical distance between the two curves on
either side of any area. At the right- and left-hand edges of the chart
the over-all dimension lines show the reader at once how to read the
chart so as to include all the various components entering into any
total which may be under consideration. The use of dimension lin^s
should be thoroughly understood by everyone drawing charts or
plotting curves, and by everyone having graphic presentations to
read. Dimension lines may add much to the clearness of a chart
without being in themselves unduly conspicuous.
CHAPTER IX
CUMULATIVE OR MASS CURVES
THE curves thus far shown have practically all been of a type
in which the thing plotted was a value or a rate per week, per
month, or per year. The tendency of such curves is to follow
a horizontal direction unless affected by conditions which cause sea-
sonal fluctuations or gradual increases or decreases. In this chapter
we shall consider curves in which the data plotted concern total out-
put, rather than the rate of output. With cumulative or mass curves,
such as are considered here, each point on the curve represents a total
output up to the time for which the last point is plotted. The figure
for each successive period of time is added to the total already re-
corded, and the new total point is plotted. Because the figures re-
lating to the last unit of time are always added to the total figures
already recorded, curves of this type are called cumulative curves or
mass curves. The tendency of a cumulative curve is to start at the
lower left-hand corner of the co-ordinate ruling and move toward
the upper right-hand corner of the sheet, according to the scale which
may have been selected.
Fig. 134 is a half-tone illustration of a cumulative-curve chart
representing the output of an automobile factory for one fiscal year
of the business. In a conference between the sales, engineering, and
manufacturing heads of this business, it was decided that the quantity
of automobiles desired was fifty per week until the first of April, then
sixty per week until the first of June, and seventy per week there-
after, giving a total production of three thousand two hundred auto-
mobiles for the whole season. It was thought that the rate of pro-
duction on the new model automobile could be increased after the
factory had been put into thoroughly good running shape, and the
schedule rate of production was accordingly increased gradually in
the manner shown. On account of the delay in getting drawings
149
150
GRAPHIC METHODS
o o
FACTORY SCHEDULE AND ACTUAL OUTPUT
o
Fig. 134. Production Schedule and Actual Output of an Automobile Factory for
One Year
The schedule is shown by the straight lines drawn according to the desired output per week. Actual
output is indicated by the waving line showing at any date the total number of autos shipped since the
beginning of the year. Note the co-ordinate paper of letter-sheet size and the scheme for marking off
weeks and months so that any fiscal year may be shown on this standard ruled paper
from the engineering department, the factory was able to ship prac-
tically no cars during the month of January, though the schedule
shows that one hundred and fifty cars should have been made that
month. During February, the factory produced cars but fell further
behind schedule constantly, as can be seen by the difference between
the angle of the schedule line for February and the angle of the actual
output line for February.
It must be remembered that with cumulative curves the angle
between the curve and the horizontal line gives the rate of production
per unit of time. The angle of the curve on the page gives much
valuable information to the reader. It is for this reason that cumu-
lative curves are sometimes much more useful .than curves in which
the rate of output is plotted horizontally from time to time. In the
cumulative curve the total output is plotted, and changes in the rate
CUMULATIVE CURVES 151
of output, judged by the angle of the curve at different times, may
be seen very easily.
During March the output curve took a rapid upward turn and we
can see from its angle that, until the end of the first week in April,
the output curve gradually approached the curve for schedule. During
the latter part of March the factory not only got out its quota of
cars each week but produced more than its quota, making up a little
for the distance it fell behind during the first part of the year. Owing
to a lack of material, because of a fire in a factory which supplied the
crank shafts for the automobiles, not a single automobile could be
shipped during the second week in April and only a few in the third
week of April. The automobile factory was busy, however, accumu-
lating a large supply of parts and assembling automobiles as com-
pletely as it was possible to do without the crank shafts which were
lacking. By measuring the vertical distance between the output
curve and the schedule curve, it will be seen that the factory was
furthest behind its schedule during the first week in May, which is
one of the best automobile-selling months of the year. If we count
the squares between the output curve and the schedule curve we see
that the factory was about four hundred and twenty automobiles be-
hind schedule at the end of the first week in May. As, however, a
large supply of parts and of nearly completed automobiles accumu-
lated while the crank shafts were delayed, the factory was able to
assemble and ship cars very rapidly when the crank shafts were finally
received from a new source of supply. The factory turned out much
more than fifty cars per week during the latter part of May and was
rapidly catching up with the schedule, until the supply of accumulated
parts was used up and the assembling departments were limited to
the rate at which parts could be produced in the machine shop. By
making every possible effort in the machine shop, the weekly rate of
seventy sets of parts was exceeded, and the curve shows that during
June and July the rate of shipping automobiles exceeded the schedule
rate to such an extent that by the end of the third week the factory
had caught up with the schedule production asked for by the sales
department. There was, however, a slump in the factory output about
the first of August, and it was not until the middle of August that the
factory was able to furnish the desired quota of automobiles regularly.
A conference held between the sales manager and the factory
manager in September resulted in a statement from the sales manager
152 GRAPHIC METHODS
to the effect that he could sell all the automobiles that the factory
could produce by the end of the year. The factory manager was told
to go ahead as fast as he wished and turn out all the cars he could
up to a total of three thousand five hundred cars. The schedule line
was accordingly changed from the second week in October, by drawing
the line so that it came out at three thousand five hundred cars at
the end of the year. It will be noticed that, though the factory had
a setback due to delayed material in the second week in October,
it was able to exceed the new schedule during the early part of No-
vember and it made the three thousand five hundred cars by the end
of the year as requested.
The foregoing account will give a fair idea of the application of
cumulative curves to problems involving output and sales. In work
of this sort, the cumulative curve is one of the most valuable aids
to the busy executive. The last point on the curve gives him the
total output since the beginning of the period for which the curve
was plotted. From the angle of the curve he can see the rate of output
for any period of time he may wish to consider. It must be kept in
mind that a cumulative curve never trends downward. It can move
only upward or horizontally. If there is no output during any period
of time the curve simply moves horizontally. Like a clock recording
time, it cannot go backward.
Though the cumulative curve proper cannot go backward, a
modified curve may nevertheless be made to show quantities which
have been added to and subtracted from, giving total net quantities.
Thus the modified cumulative curve may be used to show the quan-
tities of stock on hand, additions to stock being plotted upward and
reductions to stock being plotted downward. Any point on the curve
then shows the quantities on hand at that particular time. In mak-
ing a curve like this it is ordinarily the practice to strike a balance
of the additions and reductions for the latest period of time, and
then to change the curve only by the net amount added or taken away.
Such a curve gives not only a perpetual inventory in the last point
plotted, but it shows the quantity on hand at different seasons of the
year as a guide for future operations. A curve of this kind can be
plotted for the total number of men employed in a large organization
just as well as for quantities of goods in store rooms.
Fig. 134 was photographed from a sheet of co-ordinate paper
specially ruled for convenience in curve plotting. The paper is eight
CUMULATIVE CURVES 153
and a half by eleven inches (a standard letter-sheet size), and has co-
ordinate ruling printed in green ink with wide margins on all four
edges to allow space for lettering, scales, etc. Note in Fig. 134 that
the green ink of the co-ordinate lines shows much lighter in color
than the black drawing ink used for the scales and the curves. Though
the co-ordinate lines are distinct enough for ease in reading they are
not nearly so conspicuous as they would be if a line cut had been used
instead of a half-tone. In making a line cut, the green lines of the
paper must, of course, be printed as black and the color value of the
green lines is entirely lost. The finished line cut shows only the rela-
tive widths of lines, not relative colors. For many illustrations of
curves, conspicuous co-ordinate lines are not desired. In such cases
it is better to use a half-tone, as has been done in Fig. 134, than to use
a line cut.
In Fig. 135 we have curves for two successive fiscal years plotted
so that they may be compared easily. The double-line curves and the
dotted-line curves are plotted to show the rate of shipments, while
the heavy -line curves are plotted on a cumulative basis and give the
total number of carloads shipped since the beginning of each fiscal
year. Ordinarily it is not desirable to put on one sheet of paper curves
giving both rate of output and cumulative output, as there is danger
of confusing in the reader's mind two different types of curves. This
illustration is included simply to show the possibility of comparing
two cumulative curves for succeeding years by plotting both cumu-
lative curves on the same sheet.
It must be remembered that cumulative curves always refer to
some definite length of time and that they must always begin at the
beginning of the period for which the summation is made. Cumulative
curves do not extend outward indefinitely, but start over again at
zero with each succeeding period of time. Thus, cumulative curves
plotted by months or weeks on a long sheet of paper, for a series of
years, would be seen in the shape of saw teeth, with the highest point
at the end of each fiscal year and then a drop to zero again at the
beginning of the next fiscal year. The saw-tooth shape makes it
feasible, and sometimes desirable for easy comparison, to plot cumu-
lative curves for several successive periods of time in the same space,
as the two cumulative curves in Fig. 135 are plotted.
The progressive average shown by means of the dotted lines in Fig.
135 is obtained by averaging each month the values for all the points
154 GRAPHIC METHODS
given on each curve since the beginning of each fiscal year. For No-
vember the average includes two months, for December three months,
for January four months, etc. The progressive averages in this chart
mean comparatively little and can be of almost no assistance to the
manager studying them. The daily averages and the progressive
averages would have been much more striking if the averages for the
two years had been plotted horizontally instead of as superimposed
curves. A moving average could then be showyn continuously so that
the average would always take in twelve months without having to
start over again at the beginning of the second fiscal year. The in-
formation in Fig. 135 would have been more simple in appearance
and more quickly apprehended if it had been given on two separate
sheets of paper, the daily average curve and the suggested moving-
average curve being shown for two years horizontally on one sheet, the
cumulative curves being shown on a different sheet with the two years
superimposed on the same scale, as in Fig. 135.
It is frequently desirable to show two cumulative curves on the
same ruled sheet of co-ordinate paper so that each curve may be
studied separately and the distances between the curves noted. Thus,
in Fig. 136, the upper curve shows the amount of money loaned since
the beginning of the operation of a factory loan-department. The
lower curve, the dotted line, indicates the amount of money repaid
by the persons obtaining loans since the beginning of the department.
The difference between these two curves thus represents the amount
of money outstanding at the end of any month. At the bottom of
the chart the actual amount of money outstanding is plotted, also
in the form of a curve. On the curve showing the amount outstanding
the height of each point above the zero line represents the distance
between the two cumulative curves in the upper portion of the chart.
It is much easier to see fluctuations if the amount outstanding is plotted
in this way from the zero line than if one must gauge the amount
outstanding by reading the space between two fluctuating cumulative
curves. When data must be read by the length of vertical lines be-
tween two curves, the eye is likely to take as the distance between
the curves the shortest distance instead of the distance measured on
the vertical ruled lines.
In Fig. 136 it was very important to watch the total amount out-
standing, for the fund available for loans from the beginning of the
loan system until January, 1912, was limited to $200. From January,
CUMULATIVE CURVES
155
CARS SHIPPED
Monthly Daily
2OOO 1O
1800 9
'600 8
200
Progressive Average
per Day
Cumulative Carloads
Shipped
Adapted from Factory
Fig- T35- Carload Shipments from a Manufacturing Plant
Two separate fiscal years are compared on the chart. The right-hand scale shows monthly averages of the
number of carloads shipped per day of factory operation. The double-line curves for daily averages
and the dotted-line curves for progressive averages are read from the right-hand scale. The heavy
solid-line curves are read from the left-hand scale and show cumulatively the total number of carloads
shipped since the beginning of each fiscal year
1912, until the end of the period under consideration the fund avail-
able for loans was $500, of which $30 (reserved for a special purpose)
could not be used for the loans for which these curves were plotted.
Note that in January, 1912, the amount outstanding exceeded the
funds formerly available for loans, and thus required an increase in
the capital of the loan fund. Though the lettering of this chart is
not as clear as it should be, the chart is nevertheless an excellent
presentation of facts and a good demonstration of the utility of cumu-
lative curves.
156
GRAPHIC METHODS
Fig. 137 shows in detail for the same loan department the opera-
tions which are summarized in Fig. 136. In Fig. 137 the heavy line
shows the actual amount of money loaned each month, while the
dotted line shows the amount of money paid back each month. The
data for these two curves were later added month by month on a
cumulative basis and plotted into the two curves, "Loaned" and
Poui-mtj
eooo
TOO
600
4oo
200
zoo
200
too
r* ?*! i iii 4 1 i * M ?*i i
4
"913
Fig. 136. Total Loans. Made to Employees by a Large Industrial
Corporation and Total Amount Paid Back, Shown Monthly Since
the Beginning of Loans
The two upper curves are plotted on a cumulative basis. The bottom curve shows the
amount outstanding and is equivalent to the vertical distance between points on
the two upper curves. The capital devoted to loans is indicated, and the chart
permits easy reading of the amount of capital not on loan at the end of any month
"Paid-back," in Fig. 136. Because of the great fluctuation in the
amount loaned and paid back each month, the operation of the depart-
ment as a whole can be seen much more easily from the cumulative
curves of Fig. 136 than from the actual monthly-loan curves of Fig. 137.
In general, the cumulative curve is of very great assistance in showing
phenomena in which there are violent fluctuations such as are seen
in the loan curve in Fig. 137.
It is interesting to note in Fig. 137 that the peaks and valleys
in the curve showing the amount paid back follow ordinarily one or
two months behind the peaks and valleys in the curve showing the
CUMULATIVE CURVES
157
amount loaned. This is entirely natural, for these loans were made
only in cases of extreme emergency when employees were in tem-
porary need. This relation of two curves to each other, with the peaks
of one curve following at some definite distance behind the peaks of
another curve, is generally referred to as "lag." Students of eco-
nomics are continually finding curves which are seen to have a very
great dependence upon each other when "lag" is taken into account.
If "lag" is not considered, a great difference in the shape of the curves
might be taken to show that there was absolutely no relation between
the facts from which the curves were plotted.
Inctudva o »IOO loon
Fig- 137- Loans Each Month Made to Employees of a Large Indus-
trial Corporation and Amounts Paid Back Each Month. Number
of Accounts Opened and also Number of Accounts Closed Are
Shown on a Cumulative Basis
Note how the curve for repayment lags behind the peaks and valleys of the curve for
loans. The extent of the lag gives a good idea of the length of time loans are out-
standing. This illustration is for the same loan department shown in Fig. 136
Great care must ordinarily be taken in determining to just how
great an extent the element of "lag" enters in. The best way of de-
termining this is to plot the two curves on separate sheets of trans-
parent bond paper, tracing paper, or tracing cloth, plotting each curve
to a separate scale, if necessary, so that the peaks and valleys in the
158 GRAPHIC METHODS
two curves will be as nearly as possible at equal distances from the zero
line. It is difficult to prove a "lag" unless the scales are selected so
that the peaks and valleys in the two curves are at the same height
above zero. After the two curves have been plotted separately to
carefully selected scales, they may be superimposed and read through
both sheets of paper held in front of a bright light. As the horizon-
tal scales for the two curves are the same, it will be found, if the
curves depend upon each other without the element of "lag," that
the peaks and valleys will almost coincide. If there is "lag," it will
be found necessary, in order to make the peaks and valleys coincide,
to shift one sheet horizontally over the other so that the horizontal
scales disagree. When the paper has been shifted back and forth un-
til the nearest possible coincidence of the two curves has been ob-
tained, the extent of the "lag" may be determined by seeing how far
the two horizontal scales are out of agreement. "Lag" is an impor-
tant feature of many different sets of curves and must be kept con-
stantly in mind when curves are being compared.
In Fig. 137 the growth in the importance of the loan department
can readily be seen by considering the twelve-months progressive
moving average showing the average total monthly loans. Though
there is, in January, 1912, a very high peak which overshadows all
other peaks, the general tendency of the curve is still rapidly upward,
because of the fact that a number of high points follow each other
in close succession, each nearly as high as the peak of January, 1913,
which stands out alone with low points on either side.
The number of separate loan accounts opened and the number of
accounts closed is shown in Fig. 137 by means of cumulative curves.
The fact that the cumulative curve for the number of accounts closed
follows so nearly the angle of the cumulative curve for the number
of accounts opened, shows that the number of accounts outstanding
has not greatly increased. It also shows that since numerous accounts
are being closed, the loans are being made to other employees rather
than being repeated continually to the same employees.
Fig. 138 is a study made to determine the size of tank necessary
to supply sufficient boiler-feed water for a number of locomotives
and tugboats. The average amount of water used each day by all
the locomotives combined is given in the lower cumulative curve.
The shape of the curve shows that locomotives fill their tanks chiefly
between six and nine o'clock in the morning and between five and
CUMULATIVE CURVES
159
Fig. 138. Cumulative Curves Plotted to Determine the Minimum Size of Tank and
the Minimum Steady Flow of Water Required for a Group of Locomotives and
a Group of Tugboats Taking Boiler-Feed Water from the Same Source of Supply
Curves for locomotives and tugs are plotted separately. A third curve is then made by adding the vertical
distances of points on the two curves to get the vertical distance for points on the third curve. The
sloping straight line shows the minimum rate of steady flow. The greatest vertical distance between
the sloping line and the combined curve shows the necessary minimum tank capacity
seven at night. The points are plotted in the middle of each space
because the values are based on the average quantity of water taken
between any two hours specified in the horizontal scale. The next
curve above gives on a cumulative basis the average of the amount
of water taken by the tugboats each day. It can be seen that the
tugs take water between six and eight in the morning and between four
and eight at night, the greatest quantity of water being taken be-
tween seven and eight. In order to see what would happen if the loco-
motives and the tugs should take watet from the same tanks, the
combined curve was made for both locomotives and tugboats by
adding the quantities for each one-hour period. The easiest way to
make a combined curve when only two curves are to be combined,
is to use a pair of dividers, taking the vertical distance above zero
for each point on one curve and stepping off that measured distance
above each point on the other curve. The prick marks showing the
160
CUMULATIVE CURVES 161
distances stepped off by the dividers locate the new combined curve
so that it can be quickly drawn in. The combined curve in Fig. 138
shows at a glance that the locomotives and tugs together take water
in such manner that the greatest rate of flow from the tank occurs
between six and eight in the morning.
One problem involved in Fig. 138 was to determine the minimum
steady rate of flow into the tank and the size of the tank so that there
would always be sufficient water available. By drawing a line diag-
onally touching the hump on the curve between seven and eight
in the morning and the hump on the curve between six and seven
at night, we get at once the smallest size flow which will keep the tank
full throughout the whole twenty-four hours if locomotives and tugs
always draw out the water as the average curves shown in Fig. 138
would indicate. The actual rate per hour at which the water should
flow is obtained most easily by assuming a horizontal distance of
several hours on the scale, and then reading upward to the diagonal
line that vertical distance which corresponds with the horizontal
distance taken. Thus, if from the point on the line for 40,000 at which
the diagonal line intersects the vertical line for five a. m., we count 10
blocks horizontally to the right, we see that it takes 9.1 blocks before
we again reach the diagonal line. Nine and one-tenth vertical blocks
correspond on the scale to 45,500 gallons of water flowing in 10 hours,
so that the minimum steady rate of flow must be 4,550 gallons per hour.
The dimension marks at "C" and "D" indicate the great amount
of water used between four and eight p. m. The diagonal line drawn
parallel to the minimum-flow line shows the amount of water which
flows into the tank between three and eight p. m., thus reducing the
quantity to be supplied from the storage space of the tank to the
amount indicated on the vertical scale by the dimension mark "C".
Between six and eight a. m., when the amount which can flow into
the tank through the regular flow-pipe is limited to the quantity
indicated by the dimension mark "B", the draught on the tank is
so rapid that all of the water indicated by the dimension mark "A"
must be furnished by the storage capacity of the tank itself. The
water does not flow into the tank nearly so fast as it is taken out by
the tugs and locomotives at that particular time of the day. If we
count the squares included vertically in the dimension line "A" we
find 7.6 squares. This shows that the amount of water which must
be furnished by the tank during the rush hours cannot be less than
162 GRAPHIC METHODS
7.6 times 5,000 (the value for each square on the scale), or 38,000
gallons. The distance "A" is really the same as the vertical distance
between the point representing the average for the hour from five
to six a. m. and the diagonal line of minimum flow. The storage
capacity necessary in any case of this sort is very simply determined
.by means of curves or mass diagrams on the general scheme of Fig.
138. The measurement of the greatest distance which shows between
any depression in the consumption curve and the minimum-flow line
which joins the peaks on either side of it gives the minimum steady
rate of flow.
There is great practical value in charts like Fig. 138. In this
case the minimum-flow line determines the size of the pipe, pumps,
or other machinery which must be installed to provide the requisite
quantity of water if the water is kept running steadily all the time.
The tank capacity must be as great as the diagram demands or there
will not always be sufficient water. In practice, it would, of course,
be customary to put in a pump considerably larger than that needed
to provide the minimum flow which the chart shows to be necessary,
and the tank would also be of larger capacity than the minimum-
storage determination of the curve would indicate. The extra capacity
of both pump and tank are, however, only a safeguard against ab-
normal conditions. The graphic solution shows the exact rate of flow
and the storage capacity which would be satisfactory if the conditions
indicated by the data on the curves were to be constantly maintained.
Fig. 139 shows the application of the cumulative or mass curve
to problems of municipal water-supply. In working up data for
rainfall in different watersheds and determining the greatest possible
amount of water which can be obtained from watersheds when dif-
ferent sizes of reservoirs are used, the cumulative curve is almost
indispensable. In Fig. 139 the method is nearly identical with that
used in Fig. 138, except that in Fig. 139 we are determining the great-
est possible rate of uniform consumption from a fluctuating supply,
instead of determining the smallest possible rate of uniform supply for
a fluctuating consumption. In Fig. 139, the lines beginning at the
hump in 1870 are drawn at different angles to touch the different
humps and show various rates of possible consumption. These flow
lines are also continued in the other sections of the curve just as if
the curve had been shown continuously in one line instead of in three
separate sections. The scale for Fig. 139 is selected to show "million
CUMULATIVE CURVES 163
gallons per square mile." The scale could just as well have been
made to show the total gallons of rainfall in the whole watershed,
but it was more convenient to put the scale on a square-mile basis,
dividing the total rainfall by the number of square miles in the water-
shed.
Cumulative or mass curves are very frequently used for the study
of quantities in earth work, especially in railroad construction. Cumu-
lative curves showing the total quantities of earth removed from cuts
and the total amount used in fills can be kept to give the whole in-
formation in the most convenient form for quick reference and accurate
study.
CHAPTER X
FREQUENCY CURVES. CORRELATION
MANY business problems can be studied most rapidly and con-
veniently if the data are put in the form of frequency curves.
Though engineers have used curves for many years to repre-
sent data relating to the laws of physics, the engineer has made prac-
tically no use of frequency curves such as are used by the biologist.
This is probably due to the fact that the engineer can determine the
laws of physics from mathematical computations based on a relatively
small number of observations, while the biologist must deal with
statistical averages based upon observations and measurements in
thousands of different cases. The laws of biology are not so definitely
mathematical as those of engineering and physics. The biologist
must have more observations than the engineer if he is to draw accu-
rate conclusions.
A frequency chart is based on the number of times a certain char-
acteristic is found repeated in a large number of observations. The
number of repetitions is referred to as the "frequency". A comparison
C. B. Davenport, in Popular Science Monthly
Fig. 140. Frequency Chart Based on the Number of Ribs in Scallop Shells. Shells
Are Sorted into Different Piles According to the Number of Ribs, the Piles (from
Left to Right) Having Respectively 15, 16, 17, 18, 19 and 20 Ribs
The heights of the different piles show the relative frequency of shells having the different numbers of ribs.
Seventeen-rib shells were found much more commonly than shells with any other number of ribs. If
a line were drawn through the tops of the different shell piles, we should have a frequency curve
164
FREQUENCY CURVES
165
relating to the frequency with which different characteristics or items
are found repeated is commonly referred to by the biologist as "fre-
quency distribution", and the charts showing frequency are quite
often called "distribution charts" or "distribution curves".
In Fig. 140 a frequency diagram is shown at the right by photo-
graphing piles of shells arranged so that all shells in any one pile con-
tain the same number of
ribs. The pile of shells at
the left, having the smallest
number of ribs, contains
but three shells. In the pile
of shells at the extreme
right, having the highest
number of ribs, there is only
one shell. The middle pile
shows conclusively that the
greatest number of the shells
have seventeen ribs. There
is a fairly large number of
shells in the pile for sixteen
ribs, and a somewhat greater
number of shells in the pile
for eighteen ribs. Though
it is unfortunate that no
horizontal scale or vertical
scale is shown in the picture,
the reader will nevertheless be able to see from this illustration the
general scheme on which frequency curves are based.
In Fig. 141 a group of men have been arranged in different rows.
There is only one man in the shortest class at the left, and only one
man in each of the tallest two classes at the right. Most of the men
are of that height shown by the row to the right of the center of the
diagram. A glance at the photograph taken looking down on this group
of men shows that there are more men shorter than the most fre-
quent height than there are men taller. If an ink line were drawn as
a smooth curve to represent the outline of the whole group of men,
when arranged in rows as shown here, the top of the curve at the
end of the longest row would be called the "mode", as it would show
the type found most frequently in all the individuals under observation.
C. B. Davenport, in Popular Science Monthly
Fig. 141. Forty University Students Arranged in
Rows, According to Stature by Inches, as
follows: 56 to 57.9, 58 to 59.9, 60 to 61.9,
62 to 63.9, 64 to 65.9, 66 to 67.9, 68 to 69.9,
70 to 71.9
This illustration gives a good idea of the basis on which a
frequency chart is constructed. A rough frequency curve
could be made by drawing a line through the ends of all
the different rows of men. The curve would show a
definite peak for the height 64 to 65.9 inches. Such a
peak is called the "mode", since it shows the type which
occurs with greatest frequency
166
GRAPHIC METHODS
NUMBER OF PERSONS WORKING ON AND ABOVE THE SIXTH FLOOR
Cloak and Suit Industry Dress and Waist Industry
In the following illustrations, curves of this kind will be noticed using
the diagrammatic form rather than the actual photographs of a classi-
fied group like Fig. 141. In Fig. 141 it is regrettable that the illustra-
tion does not show a scale giving for each row the maximum and mini-
mum height of men in that row. Some scheme, of course, was neces-
sary to divide these men up into
height classes, but the reader has
no way of knowing the limits of
height for each class except by re-
ferring to the title of the illustra-
tion.
Frequency charts are some-
times made for popular illustra-
tion by drawing vertical lines to
represent the number of individ-
uals found in each class designated
by the horizontal scale. Thus, a
representation could be made for
the data of Fig. 141 by having a
horizontal scale to represent
heights, and drawing vertical lines
to a scale by which the length of
each vertical line or bar would
Joint hoard of Sanitary Control, New York City
Fig. 142. The Number of Persons Work-
ing On and Above the Sixth Floor
in the Cloak and Suit Industry and
the Dress and Waist Industry in
New York City
This chart was made first for a wall exhibit and was
later used in a widely distributed report. The
co-ordinate ruling has the shape of a New York
manufacturing building. By observing this illus-
tration from the left edge of the page the reader
may get the general effect of a frequency curve
represent the number of individ-
uals of that particular height. The
series of bars would then have the
same general arrangement as the
photograph of Fig. 141 representing the number of men actually seen.
These bar diagrams to represent frequency are not of very great use,
except possibly in advertising work where it may be necessary to get
some kind of chart which can be understood by any untrained reader.
In Fig. 142 an effective use has been made of the frequency-curve
scheme in a report intended for wide circulation among persons who
have not been trained in reading curves. The general outline of a
tall New York manufacturing building is given very clearly as a field
of co-ordinate ruling, on which the actual numbers of workers for any
floor level can be read from the horizontal scale with a fair degree
of accuracy. The numbers working below the sixth floor are very
large, and only those on and above the sixth floor are shown.
FREQUENCY CURVES
167
This allows the use of a large scale for the data of the upper floors.
In order to see the general shape of a frequency curve when plotted
with flat tops instead of peaked tops, the book may be turned so
that the illustration is seen from the left-hand edge. This chart was
drawn primarily as a wall exhibit, to be used later as an illustration
in a printed report. The general scheme is excellent and it could
scarcely be improved upon, even though the independent variable
has here been made the vertical scale instead of the horizontal scale.
Putting these data in the form of a curve such as is used in Fig. 143
would probably not be as effective for untrained readers as the black
bars of Fig. 142, ^
placed against a field ^°
in the general shape
of a New York man-
ufacturing building.
Fig. 143 shows a
frequency diagram of
the kind found most
useful in ordinary
work. The vertical
scale here represents
percentage, and the
total of all the figures
shown at the upper
part of the chart
added together is 100
per cent. Frequency
curves are very often
used, however, with
numbers rather than
percentages repre-
sented on the vertical
scale, and the vertical scale then shows the actual number in each class.
To assist the reader, the total number of observations made would
usually be recorded, perhaps in the title of the illustration. In bio-
logical work observations are usually made in vast number, to permit
making a very accurate conclusion regarding the general laws of fre-
quency for any particular subject under consideration. For a great
many problems of everyday life, however, the observations are not
2Z 24 26
38 4O 42 44
28 3O 32 34 36
AGE AT MARRIAGE
Data of Amy Hcwes, in Publications Am. Statistical Assn.
Fig. 143. Age at Marriage of 439 Married Graduates of
Mount Holyoke College who Graduated from 1890
to 1909
The vertical scale shows the percentage of the whole 439 who married
at each age given on the horizontal scale. The totals of all percent-
age figures at the upper margin of the chart is 100 per cent. If a
greater number of persons were included in a frequency curve of this
sort the curve would be less irregular and the mode would show more
distinctly
168
GRAPHIC METHODS
of sufficient number to permit the formation of any general laws.
Thus for Fig. 143 we are not justified in saying that all college women
marry at the particular ages indicated by this chart. The number
of women taken into consideration for the preparation of the chart
was not sufficient to allow any final conclusion, certainly not to justify
any general statement that college women are less likely to marry at
the age of twenty-six than at either twenty-five or twenty-seven.
Aggregate Population
Males Females
es+
65-64
45-54
35-44
30-34
25-29 {ft^R^
20-24
15-13
^^
rs
65+
55-64
45-54
35—44
3O— 34
25—29
2O- 24
15—19
O-I5
100
ao
60
20
O 2O
Per Cent.
40
60
10O
Chinese and Japanese
Males Females
65 +
55-64
45-54
35-44
3O-34
25-29
20-24
15-19
O-15
E
65 +
55-64
35—44
30-34
25—28
20-24
15-19
0-15
too
eo
so
40
20
dl Single
o 20
Per Cenrt,
Married
4O
eo
ao
100
Widowed
United States Statistical Atlas, 1900 Census
Fig. 144. Conjugal Condition of the Population of the United States in 1900 in
Proportions of the Total Number of Each Age Group
This chart was printed in color in the Statistical Atlas. Here shading is used instead of color. The arrange-
ment to the right and left of a zero line at the center makes visual comparison difficult between the data
for males and females. Note the contrasts between the upper and lower charts. Compare the upper
chart with Fig. 145
In biological work the number of observations taken is ordinarily
sufficient to permit drawing a smooth curve to represent the general
law, after a chart drawn with numerous straight lines has been made
by the method used in Fig. 143. It would not be desirable to draw
a smooth curve in the case of Fig. 143, as the smooth curve would
be misleading because of the small number of observations made.
For most business problems, and in many problems actually in the
field of statistics, the laws which affect frequency are so indefinite
FREQUENCY CURVES
169
and the number of observations so limited that it is much better to
use the straight-line method of Fig. 143 than to attempt to make a
smooth curve. Sometimes a smooth curve may only mislead the
reader, making the chart appear very accurate when in reality the
data were so crude that only the roughest approximation is possible.
Fig. 144 is copied from the Census Atlas for the 1900 Census. In
the Atlas, colors were used for the different areas which must be repre-
sented here by cross-hatching. Though these illustrations hold some
very valuable and interesting information, the information is contained
Per Cervr
1OO
under
15
15-19 25-29
20-24 30-34
Male
35-44 45-54 55-64
— --Female
over
65
Fig. 145. Conjugal Condition of the Population of the United States in 1900 in
Proportions of the Total Number of Each Age Group
Here the arrangement of Fig. 144 has been reversed so as to place age on the horizontal scale, since age
is the independent variable. Having the data expressed in curves permits much clearer interpretation
by the reader. Curves for male and for female may be instantly compared. The term "widowed"
as applied to men was used to harmonize with the preceding illustration
in such manner that it is almost impossible for the reader to get it out.
In the first place, age is the independent variable, but it has been made
the vertical scale. The information sought is the percentage at different
ages for each of the sexes, and this must be read from the horizontal
scale, in violation of one of the most important rules for graphic work.
Another bad feature of the chart is that data for male and female are
shown in the right and left direction from the center line, making it
almost impossible for the reader to compare the figures for male and
female at any age under consideration. The data for the upper half
of Fig. 144 are replotted in Fig. 145, and the reader would do well to
170 GRAPHIC METHODS
compare the two illustrations to see just how much more clear Fig. 145
is than Fig. 144.
The bottom portion of Fig. 144 is shown here by way of contrast with
the upper portion. Notice, for instance, the difference in the shape of
the chart for the female Chinese and Japanese population of the United
States as compared with the chart for females in the aggregate popula-
tion of the United States. A very large percentage of female Japanese
and Chinese are married by the age of thirty-five, but after that age
there is a fairly large percentage reported as single. It would appear
that many widows must be reporting themselves as single instead of
as widows, or the chart would probably not be so different in shape from
the chart for the aggregate population of the United States.
In Fig. 145 the scale for age has been properly placed horizontally
and the scale for percentage placed vertically. The whole population
is considered as single under the age of fifteen. The total of the figures
for single, married, and widowed on any vertical line equals 100 per
cent; thus, as the number married in succeeding years increases, the
number who are single is seen to decrease. The curves prove at a
glance that the women start to marry much earlier than the men.
Between twenty and thirty -five the horizontal difference between the
two curves shows that the women marry about four years earlier than
the men, or, in other words, taking the population as a whole, the
women marry men about four years their seniors. In considering
these curves it must be remembered that this chart is made up on a
different basis from Fig. 143. In Fig. 143 all the women who married are
recorded as married, and the top of the curve (the mode) shows at
once the age at which marriages are most frequent. In this chart, how-
ever, we are considering three things, and the chart shows the percentage
who recorded themselves as married, rather than the actual age at which
marriage occurred. The percentage of those who report themselves
married is affected by the number who are single and also by the num-
ber who are widowed. If in the later age classes, deaths of husbands
occur more rapidly than marriages of spinsters for any particular age,
the "married" curve will trend downward even though a very large
number of spinsters may be marrying at that age. It is simply a ques-
tion of balancing the death rate of husbands against the marriage rate
of spinsters. The curve marked "married" on this chart does not show
the age at marriage, but simply shows the percentage in any age class
who report themselves as married and not widowed.
FREQUENCY CURVES 171
The men marry later than the women. Many of the men marrying
over forty marry women much younger than themselves. As the hus-
bands are older than the wives, the expectation of life for the husband is,
of course, less than for the wives, and the number of widows at any age
is far in excess of the number of widowers, on this account alone. In-
dustrial accidents, war, etc., also tend to make a high death rate among
the men and cause more widows than widowers. In Fig. 145 the curve
for men has been labeled "widowed" to follow the Census Office prac-
tice in Fig. 144.
With Fig. 144 some of the age classes are for an interval of only five
years while other age classes have an interval of ten years, yet the
different lengths of interval are shown by the same distance on the scale.
For Fig. 145 the horizontal scale has purposely been made such that
the ten-year age intervals are set off by twice the distance used for the
five-year intervals. As there are very few marriages under fifteen,
the space for "under fifteen" has been made three times the space for
the five-year interval. Taking the standard life as four-score years,
the space for "over sixty-five" has been made three times the distance
used for the five-year intervals. This selection of horizontal distances
makes the curves into much more nearly their correct shape than is
possible on the Census Office chart, where five-year and ten-year
class intervals are shown by equal scale distances.
Perhaps the greatest gain made in clearness in Fig. 145 is due to
the placing of the curves for male and female on the same ruled field,
so that they can be compared instantly and correctly without need
for any right-hand and left-hand measurements such as were necessary
in Fig, 144. No claim is made that Fig. 145 is suitable for untrained
readers. Since, however, it is doubtful whether many unskilled read-
ers ever refer to the Census Atlas, it would seem desirable to use the
general scheme of Fig. 145 for clearness and convenience.
In Fig. 146, also taken from the Census Atlas for the 1900 Census,
a right-and-left measurement must be made to compare death rates
in two different years, ten years apart. The chart was drawn to bring
out the data clearly and, if clearness is not attained, the data might
just as well be expressed in columns of figures. Here again the vari-
ables have been reversed and the independent variable improperly
made the vertical scale.
In Fig. 147 the data of Fig. 146 are redrawn into two curves by
which the number of deaths occurring at different ages can be readily
172
GRAPHIC METHODS
United States Statistical Atlas, 1900 Census
Fig. 146. Comparative Proportion of Deaths at Different Ages from Pneumonia
per 1,000 Deaths from Pneumonia in the Registration Area of the United States,
1890 and 1900
The right-and-left arrangement of this chart makes comparison for the two different years almost impossible.
Contrast this illustration with Fig. 147
compared for the two years under consideration. Notice that in the
later year, 1900, deaths from pneumonia between the ages of ten and
sixty years were much less frequent, while deaths after the age of
sixty were more frequent. There was also an increase in the number
of deaths at ages less than four. Certainly the facts relating to deaths
from pneumonia for the two years are much more clearly brought
out in Fig. 147 than in Fig. 146.
There are some peculiarities in Fig. 147 which should be pointed
out. The Government figures are given by one-year intervals up to
the age of five, and then on five-year intervals to ninety-five. Fig. 147
really should have been made so as to indicate a change in the hori-
zontal scale at five years. If the chart had been made the full width
of the page it would have been possible to get room enough to show
the figures for single years at ages under five by using a space
only one-fifth of the horizontal distance used for the five-year inter-
vals. The large number of deaths at ages five to nine inclusive is
very striking on the curve. Possibly the large death rate from five
to nine may be due to the lessening of parental care at an age when
exposure becomes more frequent. By ten years of age, the children
have learned better how to take care of themselves and the number
of deaths from pneumonia comes down to about the lowest point.
Though the foregoing explanation of the large number of deaths
from five to nine years may be correct, it is probable that the figures
are more or less in error, due to the tendency to state ages in numbers
FREQUENCY CURVES
173
per 1000
20O
which are multiples of five. The peaks for the period five to nine
may be due largely to parents giving the age roughly as "five years".
In Fig. 148 the data in which the reader is interested are shown
at the peaks of various triangles. The shaded triangles on the chart
give a geometrical figure which at first glance might be considered
as a curve. It is not until after a considerable amount of puzzling
that one notices that the triangles have absolutely no significance
and that they are only a means of showing the distance from the
base line to the various points representing decrease or increase. It
would have been better if plain black bars had been used for Fig. 148
instead of the tri-
angles. Bars are so
familiar to everyone
that there would be
no danger of error in
interpretation. This
illustration was used
in a Sunday news-
paper article where
a non-technical class
of readers had to be
reached. For such a
class of readers the
solid black bars
would probably be
the most easily un-
derstood method of
presentation.
For anything ex-
cept newspaper pres-
entation, the method
of Fig. 149 would
probably be more
acceptable to the
Fig. 147. Comparative Proportion of Deaths at Different
Ages from Pneumonia per 1,000 Deaths from Pneu-
monia in the Registration Area of the United States,
1890 and 1900
Comparison of the two years can be made instantly throughout the whole
range of ages. Age is the independent variable and, hence, is shown
here as the horizontal scale. It would be better if a vertical wavy
line or some other signal were used to show the change in the horizon-
tal scale for ages below five years
reader than the solid
black bars suggested in the preceding paragraph. The curve drawn
in Fig. 149 shows a fairly uniform increase in death rates as ages
increase up to the age of sixty. The degree of uniformity in increase
is much more readily seen from the curve line than it could be shown
174
GRAPHIC METHODS
DECREASE
INCREASE
29.2
26.4-
by the use of bars. Granted that the curve of Fig. 149 might not
be understood by all the readers of a newspaper, it is nevertheless
much more desirable, even in newspaper work, than the method shown
in Fig. 148. Though Fig. 149 might not attract deep interest on the
part of a newspaper reader, it would not be likely to be misinter-
preted. Fig. 148 might serve to attract attention, but what is the use
in attracting atten-
tion unless a correct
impression is given
after attention has
been attracted?
Frequency curves
thus far considered
have permitted read-
ing from the vertical
scale only the actual
number or percent-
age observed corre-
sponding to any
point which may be
selected on the hori-
zontal scale. Thus,
in Fig. 143 (see page
167) we can read
from the vertical
scale only the per-
'Unfler Age 20 20' to 30 30 to 40
EUS
Age 40 to 50 50 to 60 60 and over
Equitable Life Assurance Society
Fig. 148. Change Since 1880 in the Death Rates of
Americans at Various Ages
The use of the separate triangles here is confusing to the reader. One is
apt to interpret the chart by the contour of the shaded areas rather
than by the points at the tips of separate triangles. Compare this
illustration with Fig. 149
centage of marriages which corresponds to any selected age on the hori-
zontal scale. In Fig. 150, however, we have the same data of Fig. 143
plotted in the form of a cumulative frequency curve. With a cumulative
frequency curve the vertical scale shows not the actual number for
any point of the horizontal scale, but the number cumulatively up
to any point which may be selected on the horizontal scale. In Fig.
143 the percentage who married at each age is given in figures at the
top of the chart. By observing the figures at the top of Fig. 143
and the figures at the top of Fig. 150, the method for plotting a cumu-
lative frequency curve will be apparent. Beginning with the per-
centages for the later ages in Fig. 143, the figures for the various
years are added cumulatively to give the figures seen at the top of
Fig. 150. The figures and the curve of Fig. 150 thus show the per-
FREQUENCY CURVES
175
cent age who married at ages greater than any specific age selected
from the horizontal scale of the chart.
Fig. 151 gives an example of a class of information which can be
shown to very great advantage by the use of cumulative frequency
curves. In an annual report of a railroad a tabulated statement of the
number of miles of different weights of rail in use at the end of the
fiscal year makes the information difficult for the stockholder to inter-
pret. Putting the data in the form of a curve like Fig. 151 lets the
stockholder see at once just what conditions are on his road, in so far as
rail weight is concerned. Thus, in Fig. 151, the stockholder may see
at a glance that a very small percentage of the rails on this railroad
weigh in excess of 75 pounds per yard, and that only about half of the
rails weigh more than 70 pounds per yard. In order to compare differ-
ent years it would be well to have a chart of this kind printed in the
S Jj 8 jj % g annual report, with
° ° ° f. Oy curves for different
ff> CO to W <V ^ -I ,, -i ,1
£ r • • M rf 8 • I years plotted on the
same co-ordinate rul-
ing, so that the
stockholder could see
by the change in the
shape of the curves
just what has been
done toward replac-
ing light rails with
heavy rails. If de-
sired, rail-weight
curves for different
railroad systems
could be shown in
the same chart, so
that the stockholder
how his
L
0
£20
15
10
£5
0) °
O
fc o
s.
5
« IO
0)
0
£
Z5
<
0) C
•00
< 1
/
' ^
/
/
/
r
/
/
,X
7"
^^
,^-
*^
SB
3 O O O O «
0 to >t in (0 j
D 2 3.3 3 ]
Fig. 149.
8 ? 8
Data of Elmer Rlttenhouse, of the Equitable Life Assurance Society
of
might see
railroad compares
with others in the
matter of rail weights .
It would have been better if Fig. 151 had, at the lower left-hand
corner, the words "more than", with an arrow pointing horizontally
to the right as can be seen in Fig. 158. In cumulative frequency curves
Change Since 1880 in the Death Rate
Americans at Various Ages
The increase in death rates for ages over forty is here shown in great
contrast with the decrease in death rates for ages less than forty.
The heavy zero line and the arrows pointing upward and downward
make misinterpretation almost impossible
176
GRAPHIC METHODS
such as this it is well to give the reader a clew that it is a cumulative
frequency curve he is observing, and the arrow with the words "more
than" accomplishes this result in a satisfactory manner.
There are two scales used in Fig. 151 with the expectation that the
reader would ordinarily use the left-hand scale when reading the chart,
using the words
"more than". The
right-hand scale
reading downward
permits the reader to
get at once the com-
plement of any figure
on the left-hand
scale, so that, by
using the right-hand
scale, the reader may
interpret the curves
on a "less than"
basis. Thus, in con-
sidering the weight,
roughly 6 per cent of
all the rails on the
system are more
than 75 pounds per
yard, and using the
right-hand scale it is
seen that, roughly,
75 pounds per yard. There
OVER
e£
*<
3 K
•» 0
3 C
3 u
1 C
5 a
3 r
- H
1 K
•> -
- o
^ -
- <
) <3
i r-
&
5 0
3 0
3 a
•) 0
3 J
1 0
5 <
•> c
3 a
•> r
3 r
- <.
J 0
3 -
3 '
I K
t K
•) 0
1 U
J -
T 0
3 r
- U
•) K
3 0
j
S,
V
\
\
V
RO
!h
\
\
\
\
\
v
\J
^
V
irt
\
^s.
"X^
0
X*
•«•,
20 ZZ 24 26 28
34 36 38 40 4Z 44
30 32
AGE
Data of Amy Hewes in Publications Am. Statistical Assn.
Fig. 150. Percentage of 439 Married Graduates of
Mount Holyoke College (Women) Graduating 1890
to 1909, who Married at Ages Greater than Any
Specific Age Selected from the Horizontal Scale of
the Chart
This is a cumulative frequency curve plotted from exactly the same data
as Fig. 143. The word "over" with the arrow at the lower left-hand
corner of the chart shows that the chart does not indicate the per-
centage who marry at any age but the number who marry later
than any specific age read from the horizontal scale
94 per cent of all the rails are "less than
is not ordinarily any necessity for using a double scale in this manner.
It is done here only to show the difference in reading a two-scale chart.
In Fig. 152 and also in Fig. 153 the cumulative curves have been
plotted on a different basis from that used in plotting Fig. 150 and Fig.
151. In Fig. 150 and Fig. 151, the curves begin at the 100 per cent line
at the top of the chart and extend downward toward the right. In Fig.
152 and Fig. 153 the curves start at the zero line at the bottom and ex-
tend upwards toward the right of the chart. The differences in the
shape of the curves will point out to a trained reader the manner in
which he must read the curves. Fig. 152 and Fig. 153 should be read
using the words "less than" instead of the words "more than". Thus,
FEEQUENCY CURVES
177
in Fig. 152 considering the curve "A", 60 per cent of all the telephone
calls of this class were answered in "less than" four seconds and 76 per
cent of the calls were answered in "less than" five seconds. Of course,
all those calls which were observed as having been answered in "less
than" four seconds are also answered in "less than" five seconds, so
that the curve is on a strictly cumulative basis. In Curve "C" it
can be seen that only 30 per cent of the calls of that class were answered
in less than four seconds, as against 60 per cent for curve "A". Though
curve " A " is higher up on the chart than curve " C ", it really represents
a smaller length of time required to answer telephone calls than shown
by curve "C". Since twice as large a percentage of the calls were
answered in "less than" four seconds, the average time for answering
calls in curve "A" is certainly smaller than the average time for curve
"C", yet curve "A" ap-
pears on the upper part of
the chart. It is confusing
to the average reader to
have curves appear on the
upper part of a chart when
they really represent numer-
ically smaller quantities
than other curves appearing
on the lower portion of a
chart. Yet this is the result
when curves are plotted on
a "less than" basis. In
order to avoid danger of
misinterpretation, it seems
desirable that cumulative
frequency curves should be
plotted on a "more than"
basis. Most of the cumula-
tive frequency curves in
this book are plotted on a
"more than" basis, so that curves involving the larger quantities or
percentages may appear on the chart above those cumulative fre-
quency curves for smaller quantities or percentages.
Fig. 152 and Fig. 153 show the application of the cumulative fre-
quency curve to commercial problems. The full explanation of these
30
EO
10
o too
60
70 80 90 100
Weight of Rail in Pounds
no
120
Fig. 151. Weight of Rails per Yard in the Main
Line Track of the Seaboard Air Line Railway
as Published in the Annual Report to Stock-
holders for the Fiscal Year Ending June 30,
1912
When using the left-hand scale the chart is read on a "more
than" basis as if the words "more than" had been used
with the horizontal scale as seen in Fig. 158. If the right-
hand scale is selected the words "less than" are used
178
GRAPHIC METHODS
two charts cannot be gone into here, but the reader can see for himself
the use of the cumulative frequency curve in studying different problems
in the telephone business. In Fig. 152 the curves show the time required
to answer calls in different cities, while Fig. 153 shows a comparison
of answering times in different classes of service. Notice that in each
of these two charts it seems that two seconds is about the minimum
which can be expected in answering telephone calls with the existing
types of equipment. Fig. 153 certainly gives in excellent manner the
comparison between the answering times for different classes of service.
It would be very difficult to convey the complex information contained
in Fig. 153 by using tabu-
lated figures only. Tabu-
lated figures would take up
as much space as the chart
and they would be less in-
telligible to any person wTho
know^s even the rudiments
of reading graphic presenta-
tions.
In Fig. 154 an attempt
was made to apply cumu-
lative frequency curves to
a comparison of wage rates
in different sections of the
United States. The chart,
however, is likely to be very
misleading, as it has been
plotted by methods which
are not in accordance with
usual practice. The variables have been reversed, and the independent
variable has incorrectly been made the vertical scale. Besides that,
the vertical scale reads downward instead of upward. In all kinds of
curve plotting it is common to have the two scales begin with zero
at the lower left-hand corner of the chart. Here the two scales begin
the zeros at the upper left-hand corner of the chart. Unless the reader
will turn Fig. 154 on its side so as to make the two zeros at the lower
left-hand corner, he may find great difficulty in interpreting the chart.
Fig. 155 shows a replot of the data of Fig. 154. Here the curves are
plotted on a "more than" basis, but it would have been better if the
90
«>flo
§70
c
&30
CO
10
°t
.-— •
— '
_- — '
_ — — —
— — — —
A
y
s
.
,<
- —
^
--
,-—
/
&•
^
/
^
/
Vc
y.f
'
/
/
/,
Telephone Service in Wisconsin
Promptness of Operators in Answering Calls
'.urves Showing Conditions inCities of VariousSiZ
Average Speed in allCities over 10,000 (£143 C
• • • • of 1000 to 10,000 I 634
\l/
/ I
65
oib ~-
Vf
C
/K
C • .... Under 1000( £76 "
,,
y\
11 C J 4 56 7 a 9 10 II l£ 13 14 IS 16 17 10 19 ft
Time of Answer in Seconds
Courtesy of Data, Chicago
Fig. 152. Time Required for Operators to An-
swer Telephone Calls in Towns of Different
Size in Wisconsin
These curves start at the lower left-hand portion of the field
and trend upward, showing that they are plotted on a
"less than" basis. Curve A shows a smaller time required
to answer calls than Curves B or C, yet the actual position
of Curve A on the chart is higher than either curves B or C.
If cumulative frequency curves are plotted on a "more
than" basis the position of several curves on a chart is
relatively such that the reader is not confused so much as
when curves are plotted on a "less than" basis
FREQUENCY CURVES
179
words "more than", with an arrow, had been placed at the lower
left-hand corner of the chart. In Fig. 155 a little study will show
the advantages of plotting curves on a "more than" basis. The reader
can see at a glance from this illustration that the wages for the western
States are very much higher than the wages in the south Atlantic
States. The position of the curves one above the other would lead
the reader at once to think of the upper curves as showing higher
wages. Here the upper curves do indicate the higher wages, but they
would not do so if they were plotted on a "less than" basis instead
of on a "more than" basis. Though it may cause some confusion
at first, it seems desirable as a general rule that cumulative frequency
curves should be plotted on a "more than" basis rather 'than on a
"less than" basis.
100
TIME IN SECONDS
1O 15 20
„ „ ANSWERING TIME OF
A OPERATORS &TOLL RECORDING OPERS.
I -Toll Recording Operators under Supervision
2- • « • without •
A- -No overload
B- - Overload
C- -
Courtesy of W. S. Glfford, American Telephone & Telegraph Co.
Fig- 153- Answering Time of Different Classes of Operators in Telephone Work
Cumulative curves of this sort give information in much more condensed and clear form than possible with
other methods of presentation. This particular chart is read on a "less than" basis, as can be seen by
the general position of the curves as related to the scales. Notice that none of the calls is answered in
less than two seconds
180
GRAPHIC METHODS
1O
20 3O
50
60
7O
80
90
10O
2
3
4
5
6
7
8
9
10
12
15
20
25
.Y
3O
<JtAS4^F4£0— WE
/B-REJD: N. AfTLANT
C-DQT. BLUlE: N,
D-BLACK: NVESTE =?N
'A
PER CENT
ME:N
£KLr*
-DASHED BL/CK: UrillTED £
DIVIS
C
EAR* tWGS
<z-
IONS
E-B|LUE: S0UTH ATLANTIC
C|ENTR4L F-
G-
•DOTTED
•DOTTED
TATES
RED: s
BLACH
CEN1
ALAS
RAL
KA
Courtesy of Factory
Fig. 154. Comparison of Earnings of Men Wage Earners in Different Portions of
the United States in 1905
This chart is almost hopelessly confused because the scales have been so arranged that the two scale zeros
appear at the upper left-hand corner of the chart instead of at the lower left-hand corner. The vertical
scale reads downward when it should read upward. See Fig. 155 for these same data redrawn
FREQUENCY CURVES
181
In Fig. 156 we have cumulative frequency curves applied to a
comparison of wages in different departments of a corporation. Here
again the words "more than" and the arrow would have been de-
sirable at the lower left-hand corner of the chart. The general position
of the curves beginning at the upper left-hand corner, however, assists
the reader to see that these curves are plotted on a "more than"
basis. A chart of this kind is of great utility in making a study of
wages. It may be noticed, for instance, in the curve for laborers,
that there is a very decided change in the shape of the curve at about
$9.00 per week. Only 62 per cent of these laborers make more than
$9.00 per week and but 80 per cent of them get more than $5.00 per
Per Cent
100
1 2 3 A 5 6 7 8 9 1O 12 15 2O 25
WEEKl^T EARNINGS - DOLLARS
.. United States „
N.Atlantic • o . S.Atlantic
•*-*-*-*- N. Central •— •— • S. Central
Western Alaska
155. Chart Showing What Percentage of the Wage Earners hi Diff erent Portions
of the United States Receive More than any Specified Amount of Earnings up to
Twenty-Five Dollars per Week
Here the scales are correctly arranged so that the two zeros appear at the lower left-hand corner. The
plotting of these curves on a "more than" basis causes curves which show the largest earnings to appear
in their proper position toward the top of thechart. Plotting of cumulative frequency curves on a " more
than" basis is usually desirable, since it reduces the chances for confusion to ths reader. This chart
could have been improved if the words "more than" and an arrow had been placed at the lower left-
hand corner on the general scheme of Fig. 158
182
GRAPHIC METHODS
O
O
Percent .
100
WAGE COMPARISON IN VARIOUS DEPARTMENTS.
100
10 12 14 16 18 20 22 24 26 .28. 30 32 34 36
DOLLARS.
Fig. 156. Comparison of Actual Weekly Earnings in Different Departments of a
Large Industrial Plant Showing Percentage of Men in Each Department Receiving
More than Any Specified Amount of Earnings per Week
This illustration was made by photographing directly from the universally ruled paper shown also in
Figures 57, 103, 130 and 134. The scales and the different titles were put on the paper with a typewriter.
Lack of steady work caused many of the laborers to get the very small earnings shown by the upper
portion of the curve marked "Laborers"
FREQUENCY CURVES 183
week. The fact that 20 per cent of all the laborers earn less than
$5.00 per week is due to intermittent employment given laborers in
this particular business. As $5.00 per week is not a living wage for
any man, the shape of the cumulative curve for the laborers at once
points out the desirability of some change in management by which
fewer men might be employed and all the men employed more steadily
than indicated by the curve for laborers in Fig. 156. Since all the
laborers were paid the same rate per hour, the only possible explana-
tion of the fact that a large number of men earn as little as $5.00 per
week must be that the laborers were not employed continuously.
More continuity of employment for a smaller number of laborers
would, in this particular case, have resulted in more money being
paid on an average to each man, so that the men would, to all essential
purposes, have received an increase in pay even though the hourly
wage rate were not increased.
Though that portion of the curves for the office forces seen at the
upper left corner of Fig. 156 appears somewhat similar to the curve
for laborers, the low earnings of a large percentage of the office force
were due to the employment of office boys and other young employees
who would have a fair chance to get a good training and grow up
with the business. Therefore, the curves for the office forces need
not attract the same attention as the curves for the laborers, who
are all full-grown men having comparatively little chance for promo-
tion.
The quick change at $11.00 per week in the shape of the curve
relating to the foremen and clerks is due to the fact that some of the
foremen in this business are paid by the hour and not by the week.
That some of the foremen receive as low as $6.00 per week and that
only 93 per cent of the foremen receive over $11.00 per week is due
to the fact that some of the men wTere off because of sickness or on
leave of absence. If the attendance of these men were more regular
the curves would not have such a decided peak at $11.00 per week.
Though Fig. 156 has been plotted on a "more than" basis, the reader
may, if he wishes, read it on a "less than" basis by referring to the
right-hand scale which has zero at the top instead of at the bottom
of the page.
Fig. 156 was made directly from typewritten copy with only the
curves and the marginal lines drawn in by hand. This same uni-
versally ruled paper has been referred to elsewhere as being con-
184
GRAPHIC METHODS
venient for general use. Here the paper is used to indicate 100 per
cent in the vertical direction, and the horizontal scale is chosen for
data unrelated to time.
No. of PerCent &
Pieces No of Orders
ZOOO IOO
I60O
1400
12OO
IOOO
800
6OO
75 100 150 ZOO
Size of Order in Number of Pieces
Fig- I57- Cumulative Frequency Curve Study of the Number and the Size of All
Orders Handled During a Ten-days Test hi a Certain Kind of Freight-handling
Work
The orders are sorted into various classes or groups according to the number of pieces called for by each
order. The limits for the various classes were fixed by the exercise of a little judgment and are shown
by the vertical lines on the chart
Curve "D" shows by small circles the actual number of orders found in each group. The curve is read
from the right-hand scale
Curve "C" shows by small circles the total number of pieces (or packages) carried by the various orders
which are found in each group. Curve "C" is read from the left-hand scale
Curve "A" shows the percentage of the total orders handled which contain more than any given number of
pieces considered on the horizontal scale of the chart
Curve " B " shows the percentage of the total number of pieces carried by those orders containing more than
any given number of pieces considered on the horizontal scale of the chart
Curves "D" and "A" refer to the number of orders or the amount of clerical work while curves "C" and
"B" relate to the number of packages handled or the actual volume of business transacted
In Fig. 157 we have an application of the cumulative frequency
curve to a class of work which would be extremely difficult to under-
stand if the graphic method were not used. In handling large quan-
tities of freight the different orders cover many diverse kinds of ma-
terial, and the jobs vary from one package up to many thousands of
packages on one order. The pieces or packages referred to here may be
anything from a single casting weighing 20 tons to a shipment of canned
goods with 5,000 boxes or cases on a single shipping order. In the
long run, however, the different classes of goods could be averaged,
and it will be found that in any one locality there would be but slight
FREQUENCY CURVES 185
change from year to year in the average size or weight of package
handled. The average weight of package might happen to be 150
pounds, and, considering a whole year, there would probably be very
little change in the average weight from month to month. Thus, for
our purpose here, the term "piece" or "package" refers simply to
the average package handled in different divisions or departments
of the work under consideration.
In order to obtain the data regarding the orders referred to in
Fig. 157, Fig. 158 and Fig. 159 the order slips are sorted into different
piles according to some "definitely thought-out plan by which there would
not be too many or too few orders in any one class or size group. A
little preliminary trial work in sorting would show the best places to
set the class limits for sorting the orders into separate piles. After
the orders have been separated into piles, it is a simple matter to count
the number of orders in each pile to obtain the data from which curve
"D" is plotted. It will be noticed from the shape of the curve that
the upper and lower limits for each class are well selected so that there
is a fairly uniform decrease in the number of orders in each group as the
size of the orders increases. The order slips in the different piles sorted
according to the size of the order are taken to an adding machine, and
addition made to obtain the total number of packages carried by the
combined orders found in any one pile or class. This gives the data from
which curve "C" is plotted. Though curve "D" shows a constantly
decreasing number of orders as the size of the orders becomes greater,
curve "C" proves that there is an increasing number of packages
handled as the orders grow larger toward the right-hand side of the
chart.
Though there are not so many orders of large size as of small size,
the small numbers of large orders nevertheless carry many more packages
than the large numbers of small orders. The executive is, of course,
interested in revenue and, for revenue purposes, as mentioned above,
all packages may be considered of the same size. Revenue obviously
depends upon the number of packages handled, rather than on the
number of orders handled. Curve "C", then, shows at a glance that
the small number of large orders are of much greater interest to the
financial manager than the large number of small orders.
Fig. 157 shows that during the ten-days test period there were no
orders in this particular class of work which exceeded two hundred
packages. Curves "D" and "C", though interesting, do not show all
186 GRAPHIC METHODS
the information which is desirable from the standpoint of management.
In order to show up the facts more clearly, curves "A" and "B" are
plotted from the same data as curves "D" and "C" respectively.
Curve "A" is plotted on a cumulative basis by the same general method
used for Fig. 150 and Fig. 151. The total number of orders for the
whole test period is first obtained, and then the cumulative number
adding up to any class-limit line on the horizontal scale of the chart is
plotted as a percentage of the total number of orders. Curve "A"
joins the zero line at 200, showing that none of the orders was larger
than 200 packages. We can see instantly that, because of the large
number of small orders, only 22 per cent of all the orders handled were
larger than twenty -five pieces per order. Only 13 per cent of all the
orders handled exceeded fifty pieces per order. Also, by reading from
the vertical scale opposite the figure for 50 per cent, we can see at once
that only half of all the orders handled carried more than twelve
packages.
In a manner similar to that used in making up curve "A", the cumu-
lative curve "B" is made up from the data relating to the number of
packages shown in curve " C ". It may assist the reader to follow these
charts if he keeps clearly in mind that curves "D" and "A" relate to
the actual number of orders of various sizes, while curves " C " and "B "
relate to the number of packages, or the amount of total business car-
ried by orders of various sizes. In other words, curves "D" and "A"
relate to the amount of clerical work needed, while curves "C" and
"B" show the actual amount of freight-handling labor involved and
measure the amount of revenue earned. Curve "B" thus shows that,
though there are not many large orders, about 69 per cent of all the
revenue comes from those orders which contain more than twenty -five
packages. Fifty-six per cent of the business (and the revenue) is due
to orders containing more than fifty packages. Twenty -nine per cent
of all of the revenue comes from orders containing more than one hun-
dred packages, yet none of the revenue for the ten-days time considered
came from orders larger than two hundred packages, since there were
no such orders during the period.
It is by reading curves "A" and "B " in conjunction with each other
that the manager may obtain the greatest information relating to his
business. Considering first the orders which contain more than ten
pieces, curve "A" shows that 55 per cent of the orders contain more
than ten packages, while curve "B" shows that 91 per cent of the reve-
FREQUENCY CURVES 187
nue comes from those orders which are larger than ten pieces each. In
other words, the manager, because of handling so many small orders,
is doing 45 per cent of the total clerical work in order to obtain 9 per
cent of the revenue. Since clerical work depends chiefly on the number
of separate orders, the manager would be able to reduce his clerical
work on this particular class of orders somewhere near 45 per cent if
he would refuse to handle orders of less than ten packages, and, by such
a decision, he would lose only 9 per cent of his revenue. For most
businesses, it would pay handsomely to neglect entirely 9 per cent of
the revenue if 45 per cent of the clerical work could be avoided. In
freight handling, the work is of course mostly under the jurisdiction
of the Interstate Commerce Commission, so that even if the manager
should wish to refuse orders of small size, he would not be permitted
to do so.
Though the small orders must be handled to give service to the
public, a chart such as Fig. 157 is nevertheless of very great assist-
ance in pointing out the actual conditions existing. When it is
seen what a large amount of clerical work is involved in handling
orders which produce only a small portion of the revenue, thought
could be given to the methods of handling small orders so that the
small orders may not cause any more expense than absolutely neces-
sary. Usually it is possible to handle small orders in a different man-
ner from the large orders, and, if the true situation is thoroughly
understood, small orders may possibly be handled by methods which
will result in much less loss than would be incurred if small orders
are handled by the same methods used for large orders.
One may see from Fig. 157 the percentages of orders and of business
or revenue for any size of order which it may be desired to consider.
Thus, taking orders which contain more than twenty-five packages,
it can be seen that 22 per cent of all the orders contain more than
twenty -five packages and that these orders carry 69 per cent of the
total business and bring in 69 per cent of the total revenue. Though
these orders of over twenty -five packages do not involve a large amount
of clerical work, they nevertheless bring in such a large percentage
of the revenue that any dividends from this particular department
must probably be paid from the revenue brought in by orders in excess
of twenty -five packages each.
The general methods used in plotting Fig. 157 have been con-
sidered at rather great length because it is felt that a chart of this
188
GRAPHIC METHODS
MORE THAN-^0" 10 20 30 40 50
100 ISO 200
Size of Order in Number of Pieces
Fig. 158. Cumulative Frequency Curve Study of the Number and the Size of All
Orders Handled During One Week in a Certain Kind of Freight-handling Work
Carried on in Two Closely-related Departments
Curve "H" shows by small circles the actual number of orders found in each size-of -order-class. Note that
at the left of the chart there are numerous orders shown in each class even though here the limits of
each class have been purposely made very close together
Curve "B" shows the percentage of the total orders handled which contain more than any given number of
- packages considered on the horizontal scale of the chart
Curves "A" and "C" are similar to curve "B" and show subdivisions of the total number of orders accord-
ing to which of two related departments handled the work
Curve "F" corresponds with curve "B" but shows the percentage of the total number of pieces carried by
those orders containing more than any given number of pieces considered on the horizontal scale of the
chart
Curves "G" and "E" are similar to curve "F" and show subdivisions in the total number of pieces accord-
ing to which of two related departments handled the work
One sub-department of the business handled the orders portrayed by Curve "A" and Curve "E". The
other sub-department handled orders portrayed by Curve "C" and curve "G". The combined work
of the two departments is shown by Curve "B" and Curve "F"
The percentage of the total number of orders handled in each of the two different departments, up to any
size of order read on the horizontal scale, may be seen by considering the distances on the chart above
and below Curve "D"
kind can be of service in a sales analysis for almost any kind of busi-
ness. A company selling fairly uniform products — shoes, for example
— could use for the horizontal scale the actual number of pairs of
shoes contained on various orders received for the test period of, say,
a week or a month. Companies having a diversified product, as elec-
trical .machinery, could best make a chart of this kind by basing the
horizontal scale on the actual value in dollars of the various orders
received. Thus, the scale could be made for orders in sizes larger,
than $50, $500, $1,000, etc. If charts are made for different depart-
ments, very interesting comparisons could be made which would bring
FREQUENCY CURVES 189
out information valuable to a corporation executive. Department
stores might also have use for charts on the general plan of Fig. 157.
Different departments could be considered by the number of orders
of various sizes. As the margin of profit in different classes of goods
in different quantity sold would be fairly well known, the manager
could get a good idea as to how much of the time of his sales force
was occupied in handling small orders, and how much in handling
large orders.
Fig. 158 is drawn on the same general scheme as Fig. 157. In
Fig. 158, however, we have the additional complexity that the freight
under consideration must be handled by two distinct departments
working in very close harmony with each other. As there is a dif-
ference in the cost of doing the work handled by the two departments,
the chart was purposely so drawn as to show the number of orders
and the number of packages handled by each of these two distinct
departments which together do all of the work under consideration.
Curves "B" and "F" show respectively the percentage of orders
and the percentage of business handled as a whole. The other curves
show the relative proportions of the orders and the business done by
the two departments. The position of the curves on the chart gives
a fairly clear idea as to whether the first department or the second
department handles the larger number of orders and the larger per-
centage of the actual business.
In Fig. 153 it was shown that, because the curves were plotted
on a "less than" basis, the curve showing the smaller length of time
appears at the top of the chart, when one would naturally expect to
find the smaller quantities of time recorded relatively toward the
bottom of the chart. In Fig. 158 the data are plotted on a "more
than" basis, and the curves are seen in their proper relation to each
other. Since the reader knows that the chart is plotted on a "more
than" basis (as can be seen by the words "more than" at the lower
left-hand corner of the chart), he may know instantly that the curves
relating to the two different departments show in their correct rela-
tion to each other. Curves "G" and "C" relate to one department,
while curves "E" and "A" relate to another department. Curve
"C" appears above curve "A" on the chart, and the reader may ac-
cordingly know without detail study that the department to which
curve "C" relates handles larger orders than the department to
which curve "A" relates. In a similar way, the upper portion of the
190 GRAPHIC METHODS
chart shows that the department to which curve "G" relates handles
a larger percentage of the total number of packages and produces a
larger percentage of. the revenue than the department to which curve
"E" relates. If this chart had been plotted on a "less than" basis
instead of on a "more than" basis, the position of these two curves
giving detailed information for the main curve "F" would be exactly
reversed, with curve "E" appearing above the heavy line "F" and
curve "G" appearing below the heavy line.
It is perhaps well to point out an error in drafting which occurred
on Fig. 158. The information most needed relates to orders containing
less than three hundred packages each. It was, however, desired to
show on the chart that none of the orders contained more than five
hundred packages, and the right-hand portion of the chart is accord-
ingly shown with a break, indicating that a section has been omitted.
As a general rule, when making a break in a drawing in this manner,
the two portions on either side of the break are made exactly as though
a piece of paper had been torn out of the middle of a drawing made
large enough to include the whole chart. Fig. 158 is incorrectly made
in that the curve lines to the right of the figure 300 on the horizontal
scale have been drawn pointing down toward the right-hand corner
of the chart where they show at the left of the break. These lines
would not appear this way if a piece of paper had been torn out of
a large-size chart. The curve lines should have continued up to the
break in the drawing more nearly on the slope seen in the left-hand
portion of the chart. The lines for curves "G", "F" and "E" would,
if correctly made, show much less slope also at the right of the break
where they lead down to the lower corner of the chart. This error
is mentioned here simply that the reader may have some guidance
if he finds it necessary to make charts including a break, similar to
that shown in Fig. 158.
It is customary in cost-keeping work to make costs which show only
an average of the cost per unit, on an average for all orders completed
during a period of time, say one month or one year. Though this
method of averaging all orders together without respect to the size
of the order is sufficiently accurate for many purposes, there are times
when such a method may gravely mislead an executive. It is almost
invariably true that small orders cost more per unit of output than or-
ders of large size. A man who makes a selling price for his work on
the average cost of small orders and large orders combined may be
FREQUENCY CURVES 191
losing money unnecessarily, because he does not realize the true cost
of work when it is done in only small quantities on different orders.
Fig. 159 proves the great variation in the cost of doing the work of
handling a certain class of freight. The position of the dots on the
chart shows that work done in orders of only twenty-five packages
costs over twice the average for orders of four hundred or over. In
keeping track of the cost of handling freight of different kinds for a
large steamship terminal and warehouse company it was found im-
possible to get reliable cost figures by averaging, day by day, the labor
cost of handling freight for preceding days. On some days all the orders
for one commodity might be small orders, and on the next day a very
large quantity of that same commodity might be handled all in one
large order, so that a gang of men could work steadily all day on that
one order. Naturally if a large gang of men work all day on one order,
the cost per package handled would be very much less than if several
different gangs were used in handling numerous orders of only ten or
twenty -five packages each. In order to get a clear view of what was
actually happening, considerable study was given to the problem and
the method shown in Fig. 159 is the result.
It was decided to make a pin board about 24 by 30 inches, on the
general scheme seen in Fig. 159, by which separate orders could be
shown on the chart by a dot to represent each order handled. As it
was desired to keep continuous records for the chief commodities, it
was not feasible to make ink marks for it would then be necessary
to start over again frequently with a completely new sheet of paper.
To overcome this difficulty, short pins were used having spherical
glass heads only 3/32 inch in diameter like those seen at the right in Fig.
186. The co-ordinate paper for the chart itself was mounted on three
layers of corrugated straw-board, having the ribs of the middle layer at
right angles to the ribs of the two outside layers, as described in Chapter
XII. A binding of gummed cloth-tape around the edge of the board
gave a neat appearance and assisted to preserve the boards during
rough service and long use. These boards were very light, yet remark-
ably strong on account of the corrugations running in both directions.
One cost clerk could not possibly figure out the cost of all orders
and all commodities handled each day. The cost method was more
in the nature of an automatic inspection system or check, so that the
general efficiency of the work done by numerous gangs and hundreds
of men could be judged by what might be called occasional analyses
192
GRAPHIC METHODS
stribution of orders by size of order
C — Average cost per package fbr orders of various sizes
8 c3 »H «-a <u
/I °
S
O 3 JS 03-0
•- 55 *o ec a a
g »H 3 0 cS
i
'Is
(
J
0 OT° ||^
f
n*
s
0
b § ° 2 i
i
1 1 °
\
*
/
CO
*]
• «a u o
/
o
s
o
o
o
s
8
o
)
3
§*O p O +j
/
•
,
4> Jv ^ M §
•»H ^^ "Zrt ^ d
4_) 3 O £3
1
C£* O >~ -• S
O ^ ?5 a> 2> ^°
8 o 5 t* ** a
I
|O «-g 2
/
Q O O § * .2
g O TS pq £•£?
/
f
.
1
r
/
•
0 50 100 150 eOO 250 300 350 400 .450 500, 55O 6OO 65O 70O
Number of PacKages in Order
?. 159. Phi Board for Determining the Direct Labor Cost of Handling Different Kinds
ship Terminal. This Cost Method Takes into Account the Number of Packages Hanc
Naturally Have a High Cost per Package
separate board is used for each commodity that is handled frequently enough to justify a study of the labor cost
straw-board with a binding of gummed cloth tape around the edges. Boards each have a sheet of co-ordinate p
surface. Short pins with spherical glass heads are pushed into the board until the heads touch the paper. Wi
continually without danger of pins falling out and spoiling the accuracy of the record
f
/
f>
I
V
A — Percentage d
R _ nietrMHiitfnn r
.
•
m
s
jf
J
A
*
*
s
/
^
/
•
jS
/
s
2
®
/
——
^
s
o
x
q
•
L
s
~~~
^^
voOOOOOOO O O O C
1
So
—
•t
•
9
1)
£
.
.1
M
1
1 •
-++-
<•>
(
4
•
<
1
0
4
•
•
2
1
*
d
1
,-<*
(O
•
1 •'
•
. I
vv
•r
1
fm '
.'
L*
i *
^ «
<!
.
.
1
•
100
••
JV
• '
•
•
c
•
.
1
U^
t
•
*
i
r<i>f-~
5 v> o «o o 10 o
D iri in ^ 'fr «o" co'
10 0
04 C\i
10 o 10 c
ui
FREQUENCY CURVES 193
taken at random. Because of the numerous commodities which were
handled on which it was desirable to watch the cost of freight handling,
the cost clerk figured the cost of any one commodity perhaps only one or
two days in a month. Each morning the cost clerk would sort out
all the labor tickets relating to some one particular commodity which
had been handled on the preceding day. The cost per package would
be figured up for each order ticket and, in the board reserved for that
particular commodity, a tall pin would be placed for each order com-
pleted the preceding day, showing by the position of the pin the number
of packages on the order and the cost per package of handling that
particular order. In considering the pin marked 8 at the right of Fig.
159 we can see that it represents an order for 900 packages and that the
cost per package was 1.1 cent. After some time in operating a pin
board the position of the various pins on the board would show in the
general form of a curve, and would indicate the cost of handling freight
of that particular commodity in lots of different sizes. Since commodi-
ties received from ocean ships are usually packed in some standard
size of bales, boxes, or bags, the pin method of charting cost is a remark-
ably reliable one.
The pin board can be of great assistance to the general superintend-
ent. As the cost of handling certain orders for certain commodities for the
preceding day is known about eleven o'clock each morning, the super-
intendent can look over the boards and note the special tall pins which
show the exact cost of various orders handled. Thus, a superintendent
seeing a board of the kind described would know that on the preceding
day those orders had been completed which in Figure 159 are shown by
numbered dots. His attention would be drawn at once to the orders
represented by dots numbered 4, 5, 6 and 8. These dots show costs
much above the average cost recorded for orders of those sizes. The
cost clerk could furnish the order numbers of these particular orders
and could also give the names of the foremen who had been in charge
of the work. The superintendent could then ask for an explanation
as to why these orders had cost much more than the work should have
cost for lots of the size handled. Considering dot 6, notice that the
average cost for 500 packages is about 0 . 80 cent, but the order repre-
sented by dot 6 cost 1.50 cent per package, almost twice what it should
have cost. Though dot 4 shows considerably above the average dots
for 100-package lots, the percentage excess is not so great as in the case of
dot 6. Dot 4 shows a cost of about 2.20 cents, while the average cost
194 GRAPHIC METHODS
for 100 packages is about 1.25 cents. What the superintendent wants
to know is the percentage excess in the cost above what the chart shows
should be the normal cost for any number of packages under considera-
tion. The chart brings out this information very clearly. Since the
superintendent can take the matter up with the various foremen before
noon of the day after the work was completed, the foremen soon get
the feeling that the superintendent knows what the cost should be, and,
if anything happens to prevent work being done cheaply and quickly,
the foremen are likely to report the conditions at once to see if assistance
can be given them so as to keep the cost low.
After the superintendent has seen the pin boards each morning, the
long pins represented by numbered dots in Fig. 159 are removed and in
their places are put the short glass-head pins having shanks so short
that the pins may be pushed into the straw-board until the head of the
pin touches the co-ordinate paper. The pins are then quite secure,
and the boards may be worked upon and handled month after month
without danger of the pins becoming lost from the boards. The
ordinary type of tall pins or tacks used with wooden boards would not
be at all satisfactory for this class of work, as it would be impossible to
work with such boards containing thousands of tacks without knocking
the tacks loose, so that they would be in a continuous process of becom-
ing lost — much to the detriment of accuracy and to the disgust of a
cost clerk. The short glass-head pins pushed in until the heads touch
are very convenient and they give a thoroughly accurate record.
As above mentioned, cost boards of the kind described would not
be satisfactory if made with ink dots because the boards would soon
have so many dots that information would be no longer easily obtain-
able. By using the glass-head pins it is feasible to change the color of
glass heads used on any board each six months. The position of the
pins of different color would then show clearly whether work was being
done more cheaply than it had been done in preceding periods of time.
Thus, if any particular campaign were made to reduce the cost for
small orders by handling small orders on some different method from
that previously used, the pins near the left-hand side of the board might
appear considerably lower down on the chart than the pins of the color
which had been used in the six months preceding the change in method.
When the board gets so full of pins as to make the pins crowded it
is a very simple matter to remove from the board all of the pins which
were inserted in the most remote period of time. Thus, it might be
FREQUENCY CURVES 195
found feasible to keep on the chart pins relating to four different periods
of six months each, so that every six months one color of pins would be
removed from the board and the pins removed would be those which had
been placed in the board two years previously. A board would then
show at all times the record of cost in handling this particular commodi-
ty during the last two years. Boards used where pins must be put
in and taken out very often may be faced with cork composition so that
the pin holes may injure the surface as little as possible. Where pins
are not to be changed very frequently, the straw-board covered with a
layer of cloth before the co-ordinate paper is mounted will be found
entirely satisfactory.
In the upper portion of Fig. 159 is shown a summary chart of the
data contained on the pin board itself. Curve "C" is a smooth curve
drawn through the center of gravity of all pins on any vertical line
which shows the size of order. It will be noticed that the cost decreases
very little when orders become larger than three hundred packages,
but for this particular commodity with the methods of handling used,
the cost increases rapidly as orders decrease below three hundred pack-
ages. Knowing the revenue obtained for doing the work, it is a simple
matter to determine from the curve the smallest size of order of this
commodity which can be handled under average conditions without
incurring a loss. If the revenue for Fig. 159 were 1.5 cents per package
it could be seen at once that (since the overhead expenses are not con-
sidered) there must certainly be a dead loss on orders containing less
than sixty -five packages each. If the overhead expenses are taken
into account as well as direct labor, there would be shown a loss on
orders of larger size, probably up to one hundred or one hundred and
fifty packages. Assuming that a loss occurs on all orders shown on
Fig. 159 up to the size of one hundred and fifty packages per order,
the number of dots to the left of the line for 150 on the horizontal scale
indicates just how great the total monetary loss would be.
Curve "A" in Fig. 159 shows the percentage of orders which contain
more than any specified number of packages selected on the horizontal
scale of the chart. Curve "B" shows the percentage of the total
packages which are found in orders containing more than any specified
number of packages selected on the horizontal scale of the chart.
Curve "A" indicates the amount of clerical work involved, and curve
"B" shows the amount of actual labor and the amount of revenue in
exactly the same manner described for Figures 157 and 158.
196
GRAPHIC METHODS
X
N\
Curves "A", "B" and "C" are shown in Fig. 159 only by way of
proving the utility of the pin-board method of keeping costs where there
is a large variation in the size of the orders worked upon. The illustra-
tion shows these curves superimposed on the pin board only to save
% space in printing.
In Fig. 160 is shown a
chart which may help to
make clearer the general
principles used in drawing
the charts seen in Fig. 157,
Fig. 158 and Fig. 159. Fig.
160 shows the appearance
of the curves if there are
the same number of orders
in each class or group and
if all classes or groups are
of uniform size. It makes
no difference in the shape
of the curves how many
orders there may be if those
orders are always uniformly
distributed throughout the
whole length of the hori-
zontal scale of the chart.
It would perhaps have been
better if Fig. 160 had been
so drawn that the length
of the vertical scale would
be the same as the length
of the horizontal scale. The actual shape of the curve line referring
to the percentage of business or the percentage of the total number
of pieces would then be free from any possible distortion which it may
have received because of the vertical scale being of less total length
here than the horizontal scale.
It is especially interesting to compare Fig. 160 with Fig. 159.
In Fig. 159 the reader may easily see for himself that there are many
more small orders than there are large orders, because the pins are
largely concentrated toward the left-hand side of the chart. It is
this concentration at the left-hand side which has so greatly affected
MORC THAN — »- O IO ?Q 3O 4O 50 6O 70 SO SO 1OO
Fig. 1 60. Chart to Show the Theoretical Shape
of Cumulative Curves for the Percentage of
Total Orders and the Percentage of Total
Business if There Is a Uniform Number of
Orders hi Each Class or Group
It makes no difference in the shape of the curves, as long as
all classes contain the same number of orders, whether there
is one order or one thousand orders in each class between
vertical lines
The straight line shows the percentage of orders which contain
more than any given number of pieces considered on the
horizontal scale of the chart
The curved line shows the percentage of the total number of
pieces carried by the orders which contain more than any
given number of pieces considered on the horizontal scale
If there is not the same number of orders in all groups or zones
the curves will take some other shape and the shape will
depend on the peculiar distribution of orders as may be
seen in Fig. 157, Fig. 158 and Fig. 159
FREQUENCY CURVES
197
•
the shape of curve "A" and curve "B" in Fig. 159. By comparing
Fig. 160, we can see that if the distribution of orders in Fig. 159 had
been uniform, curve "A" would have been a straight diagonal line
and curve "B" would have been a curved line bowed upward instead
of bowed downward. too
Though Fig. 161
somewhat resembles
Fig. 160, it is never-
theless constructed on
an entirely different
plan. In Figs. 157,
158, 159 and 160 the
independent variable
related only to size
of order. For charts
of the type shown in 30| | ../
Fig. 160 the inde-
pendent variable is a
percentage. The de-
pendent variable is
also expressed as a
percentage.
Imagine the whole
population placed in
a long line and ranked
according to income.
The people in this
line could be counted
off into several equal
90
80
7O
*
|60
Z
*5 50
040
zo
10
10
eo 90 too
— EQUALITY PRUSSIA 1892. PRUSSIA 1901
M . O. Lorenz, In the Publications, the American Statistical Assn.
Fig. 161. Curves to Show the Percentages of the Total
Population of Prussia hi 1892 and hi 1901 that Re-
ceived Various Percentages of the Total Income as
Considered on the Horizontal Scale
If incomes were all equal the relation of population and income would be
expressed by the straight diagonal line. The amount of inequality
between various incomes is shown by the amount the curve diverges
from the straight line. There was greater inequality of incomes in
Prussia in 1901 than in 1892
groups so that each
group would contain say 10 per cent of the total number. It would
then be simple to compute the income of each group as a percentage
of the combined income for all groups. The resulting group percentages
would be plotted cumulatively as the dependent variable on a chart
for which percentages of population would be the independent vari-
able. Fig. 161 unfortunately shows the independent variable used
for the vertical scale. A better arrangement may be seen by observ-
ing the illustration through the back of the paper with the two zeros
appearing at the lower left-hand corner.
198
GRAPHIC METHODS
Diagrams made on the scheme of Fig. 161 are of very great assist-
ance in studying such matters as the distribution of wealth for any
country. The subject of wealth distribution is so complex that unless
data are expressed graphically there would be very serious difficulty
in getting a true understanding and appreciation of the different
factors involved. In Fig. 161 we have the curves for two widely sep-
arated years plotted side by side, so that we may tell from the general
shape of the curves whether the distribution of wealth is approaching
uniformity of tending in the direction of great concentration in the
hands of a few people. The more nearly the curve approaches a straight
line the more nearly wealth is distributed uniformly among all the
tz
0
0
t. 8
I
O 1000 2.OOO 3.OOO 4OOO 5.OOO 6.OOO 7.OOO 8,000 9.OOO IO.OOO
RcrbJnci of" Truck m Pounds
• Report by Operator o Estimate by Manufacturer
* Average reported Figure
H. F. Thomson, Massachusetts Institute of Technology, Vehicle Research
Fig. 162. Cost of Gasoline in Cents per Truck-Mile for Different Sizes of Motor
Trucks
Since motor trucks are rated by the manufacturers in multiples of 1,000 pounds, the dots representing the
records of different trucks naturally fall on the lines spaced by 1,000-pound intervals on the chart.
The solid line is drawn through points at the "center of gravity" of all dots for any vertical line on the
chart and represents the average condition as reported by truck operators. The dotted line is drawn
through points on the chart for data furnished by the manufacturer as his estimate of good practice
A curve of this general type, proving a close relationship between two variables, may be called a correlation
CORRELATION 199
members of the population. In Fig. 161 the line was more bowed
in the later year than in the earlier year, and the conclusion may ac-
cordingly be drawn that wealth in Prussia tended toward further con-
centration in those years intervening between 1892 and 1901.
In Fig. 162 a study has been made to see how the gasoline con-
sumption of motor trucks varies in trucks of different sizes. The hori-
zontal scale shows the rated size in pounds of the trucks under con-
sideration. On the vertical scale, the cost of gasoline is given in cents
per car mile. The data of the different motor trucks were indicated
by separate dots on the chart. The solid line was then drawn through
a point which represents the center of gravity of all the dots on each
vertical line. The total number of dots on this chart is rather small.
Too much dependence cannot be placed in the resulting curve, as
special conditions may have affected some of the records so as to
cause the dots to be misleading. Thus, considering the two dots
which are given for trucks of 2,000-pounds capacity, it will be noticed
that both of these dots are far below the position on the chart which
one would expect the average to occupy if one should judge by the gen-
eral tendency of the curve as a whole. It may have happened that
the particular trucks which these two dots represent were run with
very light loads, thus making the gasoline consumption lower than
would naturally be expected for trucks of that size. In Fig. 162 the
object is to determine what relation, if any, exists between the cost
for gasoline and the size of the truck.
"Correlation" is a term used to express the relation which exists
between two series or groups of data where there is a causal con-
nection. In order to have correlation it is not enough that the two
sets of data should both increase or decrease simultaneously. For
correlation it is necessary that one set of facts should have some defi-
nite causal dependence upon the other set, as seen in Fig. 162.
Correlation studies can frequently be of assistance in business prob-
lems. A manufacturer of machinery has recently revised many of
his manufacturing and selling policies from the information obtained
from a chart showing the relations of cost and selling price of his
equipment to the actual size of the equipment. On the horizontal
scale of charts used for this study the size of the apparatus was shown
according to its actual working capacity. In a vertical direction a
scale was selected for the cost of the apparatus and for its selling
price. Dots were then placed on the chart in a manner similar to
200 GRAPHIC METHODS
Fig. 162, and a line was drawn on the chart through the different dots
representing the factory cost of the machinery. The line was not at
all straight and the chief executive spent much time in finding out
why there were so many variations from uniformity. He found,
among other things, that some of his machinery had not been re-
designed for several years, and that the weight of material used was
much greater than necessary when taking into account the greater
strength of steel and iron made by modern processes. Though mate-
rials of the modern kind were being used to a large extent in his ma-
chinery, the weight of material had not been reduced and there was
more weight of employed material than was actually necessary if new
designs were made. Another cause for fluctuation in the curve line
was found in the quantities in which the product was manufactured.
Some sizes of apparatus were particularly suitable to the public,
and on these sizes the quantities were much larger than on other
sizes. The sizes more commonly sold were naturally better equipped
with jigs and tools than other sizes, and for that reason the cost was
lower than would otherwise be expected. After the cost curves had
been thoroughly studied for different kinds of apparatus, the selling-
price curves were drawn in on the same sheets. It was found that
for selling prices, also, there were numerous inconsistencies which
could be corrected with advantage to the company. Though some of
the peaks and valleys of the selling-price correlation curves were to
be expected, there was no justification for others and a little concen-
trated study brought forth methods by which the selling-price curves
could be changed materially with advantage to both the producer
and the consumer.
In the study of physics and of experimental engineering, there are
many times when a correlation curve is of assistance in the discovery
and understanding of the laws of nature. For Fig. 163, many ob-
servations were made and recorded on a sheet of co-ordinate paper.
After sufficient observations had been made throughout the whole
range of the horizontal scale, smooth curves were drawn which would
most nearly represent the various dots plotted. In drawing curves
of this kind, care should be taken to have each portion of the curve
as nearly as possible at the center of gravity of the dots in any vertical
section of the chart. Accuracy is not necessarily obtained by having
the same number of dots on either side of the curve. If there are
only three dots at some vertical line, it may be that two of these dots
201
would be close together and their combined weight must be considered
as compared with one dot which may be some distance away. As a
simple rule, consider the dots in any vertical section of the chart as
though arranged on a see-saw, as used by children, and then shift
the point through which the curve line is to be drawn so that the
see-saw will just balance evenly.
eOjOOOrieoo-
•70,000 1400
60,000
50,000 1000- ;
£ 40,000 -800
ft
3
s
30,000 -600
80,000 -iOO
10,000 -200 ef
1200-
X
ss
3
XToO
7
Velocity of circulating water -=ft. per sec. '— *FW
Gee. 4. Onot, in Journal American Society of Mechanical Engineers
Fig. 163. Relation of the Rate of Heat Transmission to the
Velocity of the Circulating Water in Surface Condensers
Correlation charts of this type have sometimes been called "shot-gun diagrams "
The investigator makes a dot for each observation recorded, and then judges
from the arrangement of the dots whether there is any general law expressing
a relation between the two variables studied
Curves like those seen in Fig. 163 may be sketched in free-hand,
or they may be much more conveniently drawn by using the irregular
or so-called "French curves" which may be obtained in any store
selling drafting instruments or artists' materials. As it frequently
happens that an irregular curve available does not exactly fit the dots
through which the curve line is to be drawn, care must be taken to
202
GRAPHIC METHODS
shift the irregular curve along and draw only short portions of the
curve line at any one stroke of the pencil or pen. Care in shifting the
irregular curve will permit drawing a clean, smooth curve line, even
though the irregular curve used is quite different in shape from the
curve line which is drawn.
69-
•
«x
x^
|
-^
•5
^
5" *"
^
V
'e
I!
A'
^
to »»
I.
IT r,
>^
^
•
x*^
^
Q °
§ 60
f
xX
^
1
^
^0
o
6S M 54 W W 57 6« ft» 60 01 69 63 «4 65 66 67 60 69 TO 71 78
Mother' $ Span (-If) in inoA^s.
Fig. 164. Correlation Curve Showing Probable Span of a Daughter from Finger Tip
to Finger Tip, for any Given Span of the Mother. 1,370 Cases were Studied
in Making up this Chart
Here the dots for the 1,370 observations are not all shown. The dots seen represent the averages of all
cases studied in each 1-inch range of mother's span according to the horizontal scale. The curve line
is then drawn through these dots. Instead of using the curve line, the mathematical relation may be
expressed by the formula D = 34.18 + .473 M
This chart would have been easier to interpret clearly if both the vertical and the horizontal scales began
with the same figure, say 51 inches. The reader is not apt to notice that the vertical scale here begins
at 58 while the horizontal scale begins at 51
Curves like those seen in Fig. 163 are properly drawn as smooth
curves because they are based upon some definite laws of nature.
It is only because of the crudity of the observations of mankind that
the dots are so widely scattered. If human knowledge were sufficient
to obtain measurements with exactness, curves for data relating to
the laws of nature would fall exactly on points plotted according to
the observations and there would be no difficulty in getting smooth
curves. The curves in this book are nearly all plotted from statistical
data for which there are ordinarily some hundreds of variables, of
which many do not follow any definite laws of nature. For most
statistical work it is much better to join the points showing the ob-
servations by straight lines without any attempt to draw smooth
CORRELATION 203
curves. Smooth curves would by their smoothness imply a degree
of accuracy in the data much greater than would ordinarily be justi-
fiable. By using the straight lines instead of the smooth curves to
connect points, the reader is warned that the chart represents facts
as found, rather than facts which are assumed to be in accordance
with any definite laws. Where smooth curves are proper, as in Fig.
163, it is feasible to have a mathematical formula to represent the
shape of the smooth curve. As the determination of mathematical
formulas to suit the shape of any curve is a whole study in itself, there
will be no attempt to cover that subject in this book.
Biologists have constant use for correlation curves. Fig. 164
shows a curve used in the solution of a typical problem such as biolo-
gists are constantly attacking. It was desired here to find out what
laws govern the physical characteristics of the offspring when certain
characteristics are found in the mother. In all, 1,370 cases were
measured, both mother and daughter, to get the data from which
Fig. 164 was plotted. All the cases were classed according to the
span of the mother, with the class limits made 1 inch apart. A single
point was plotted on the chart as an average for each class. A curve
line was then drawn so as to represent most closely the data shown
on the chart, and it is seen that the curve is a straight line. There were
naturally fewer observations at either end of the chart, for the very
small spans and for the very large spans, than for the intermediate
spans. It was probably because of the small number of observations
at either end of the curve that the dots there are so far away from the
curve line. If more numerous observations were taken it is probable
that all the averages would fall more closely on the curve line than seen
in Fig. 164.
The ordinary course of procedure in making a correlation chart
is to plot all the observations by the method seen in Fig. 163. Some-
times, however, the observations are so many as to make an extremely
confusing chart if the observations are shown in the form of separate
dots. In Fig. 164 the observations in any 1-inch class have been
averaged and all the observations in one class are represented by a
single dot. In Fig. 165 the dots would be very numerous, so numerous
as to make it not feasible to show them on a small size chart. For
Fig. 165 it was desired to show the maximum income and the minimum
income, as well as the average income. Instead of showing all the
dots on the chart, cross-hatching was used to represent the area in
204
GRAPHIC METHODS
VCARS AFTER RECEIPT OF B.S. DEGREE OR COMPLETION OF FOUR YEAR COURSE
Courtesy of Data, Chicago
Fig. 165. Income of Graduates of Worcester Poly-
technic Institute at Various Years After Graduation
Instead of showing hundreds of dots to represent the data received from
different graduates, the chart was simplified by shading the area
representing the range of income. The shading thus shows the maxi-
mum and the minimum incomes. This general method is a worthy
one
which the dots fell. The upper edge of the cross-hatching shows the
maximum of the incomes, and the lower limit of the cross-hatching
shows the minimum of the incomes reported for different years after
graduation. The reader can thus get the whole story at a glance
without being con-
fused by the com-
plexity which would
result if all the dots
were shown. Atten-
tion should be called
to the fact that the
curve of average in-
come falls much
closer to the bottom
of the shaded area
than to the top of the
area. This fact shows
that, though there
are several graduates getting high salaries much above the average
income, nevertheless, if all of the dots were shown, most of the dots
would fall below the average line rather than above the average line.
A few extremely large incomes near the maximum line of the chart could
greatly raise the average line but still most of the dots would be found
beneath the average.
Fig. 166 is a very interesting correlation chart. Here a single dot
has been used for each observation and the dots are shown in the
chart. Instead of showing each dot in its exact position, the dots
have been grouped so that all the dots are arranged uniformly inside
of squares formed by co-ordinate lines spaced 10 units apart in the
scales for examination marks. Classification by class limits 10 units
apart on the scale of marks is sufficiently accurate for all practical
purposes, as is proved by the gradual change in shading on the chart
as a whole. With few observations it might be desirable to show dots on
the chart to actual scale rather than in classes by tens.
Ordinarily a line drawn like the heavy wavy line in Fig. 166 would
be so placed that the points on the line would be at the center of
gravity for the dots vertically on either side of the line. Here, however,
the line is so drawn that there are an equal number of dots on either
side of the line, at right angles to it at any point throughout its course.
CORRELATION
205
Notice that in the upper portion of the chart the line shifts across the
equality line, showing that some of the more brilliant girls obtain
higher marks in arithmetic than they do in English. The lower por-
tion of the chart shows that the larger number of girls get considerably
better marks in English than in arithmetic, and that this is a general
condition to be expected. In the case of those girls who do well in
both English and arithmetic, there seems to be improved facility in the
field of arithmetic.
100
10 ZO
3O 40 SO 6O
ENGLISH MARKS -
70 CO 90 1OO
Data of W. Garnett in the Journal of the Royal Statistical Society, 1910
Fig. 166. Examination Marks Obtained by 9,396 School Girls in England
Each girl is represented by one dot showing to scale the grade in English and the grade in arithmetic. The
dots are arranged uniformly inside of squares formed by co-ordinate lines spaced ten units apart in the
scales for marks. The straight diagonal line drawn from zero shows equal ability in the two studies.
The heavy wavy line is drawn through points having an equal number of girls represented on either
side of the line, and its position proves that girls have much more ability in English than in arithmetic.
206
GRAPHIC METHODS
The data of Fig. 166 are shown by another method in Fig. 167.
Though Fig. 167 appears to represent a solid model, there was m reality
no solid model made in order to obtain this illustration. By using iso-
metric paper a chart like Fig. 167 can be made with comparatively
little work. Isometric paper has lines ruled on the paper right and left
at an angle of 30 degrees to the horizontal. By selecting a vertical
scale to portray by separate columns the number of girls represented
in any square of Fig. 166, it becomes a comparatively simple matter to
draw the illustration. The various necessary lines can be drawn free-
hand in pencil on top of the isometric co-ordinate ruling, until the chart
is completed; then the various lines can be inked in to get the final
effect seen in Fig. 167. The total number of girls represented in any
column is shown by the figures at the top of the column.
Data of W. Garnett in the Journal of the Royal Statistical Society, 1910
Fig. 167. Examination Marks Obtained by 9,396 School Girls in England
This illustration was made from the same data as Fig. 166. Here the number of girls in any square is shown
by the height of the vertical column drawn to scale.
The arrangement of scales here is different from that in Fig. 166 as will be noticed by observing the direction
of the arrows
CORRELATION 207
The reader should note carefully that the scale arrangement of
Fig. 167 is entirely different from that used in Fig. 166. In Fig. 166, the
two zeros fall together as they ordinarily should do in chart work of
this sort. In Fig. 167, however, the two scale zeros are not together
and the reader is accordingly prevented from interpreting Fig. 167
directly from the location of dots seen in Fig. 166. It would seem as
though a better chart could have been made if the isometric chart,
instead of being as in Fig. 167, had been arranged with the two zeros
together. Such an arrangement would have permitted easier interpre-
tation, for the reader would have secured a more close similarity
to Fig. 166. Another possible arrangement which would have been
better than that used in Fig. 167 would put the two 100 per cent marks
of the scale together, with the zero marks at the diagonally opposite
corners. A chart of this nature would show as two mountain peaks,
one on each side, with a valley in the center.
Where an actual model is desired more than an illustration, a very
convenient, yet cheap, arrangement can be had by stringing beads on
separate wires, each mounted in the center of ruled spaces, like those
shown in Fig. 166. The number of beads on each wire can represent
to scale the data for the particular square at the center of which the
bead wire is placed. The heights of the columns of beads on the differ-
ent wires would then show clearly the facts for any one section of the
field in a manner similar to that of Fig. 167. The beads would probably
be more generally understood by an untrained person than the isometric
drawing of Fig. 167, and it is for this reason that the scheme is mentioned
here. The arrangement by columns seen in Fig. 167 is satisfactory
for the trained reader, but the separate beads on wires would probably
give a less abstract impression, more easily grasped by the average
person.
CHAPTER XI
MAP PRESENTATIONS
MAPS marked, colored, or shaded in different ways, or used in
conjunction with pins or other signals, form one of the most
convenient means of conveying information. Such maps may
be used to advantage in a surprising variety of ways, only a few of
which can be mentioned here.
Engineers who have with great labor prepared complete plans,
specifications, and estimates for some proposed improvement are fre-
quently disappointed that they cannot arouse enough enthusiasm in
the proposed scheme to obtain the approval of the government or
municipal officials, or members of a corporation board of directors, who
must vote in favor of the plan and appropriate the money necessary to
carry it into effect. It is always difficult to get non-technical persons
to take an interest in proposals which are shown only by blue prints
and ordinary maps. Architects realize this so well that it is common
practice among them to submit carefully prepared wash-drawings to
show the appearance of the building for which they are submitting
plans. Most engineering work cannot be easily represented by wash-
drawings, and the engineer is accordingly somewhat handicapped as
compared with the architect in arousing interest in his project.
Fig. 168 shows a picture developed by H. W. Holmes, Chief of the
Bureau of Highways and Bridges, of the city of Portland, Oregon, to
present his plans advantageously to the common council and the tax-
payers to obtain their approval for the expenditure. A photograph
of the actual site of the bridge was made, and then the picture of the
bridge was drawn in by hand on the photograph. Most engineers
submitting plans for an improvement of this kind would send only a
set of blue prints and perhaps a map marked to show the location of
the proposed bridge. A picture like Fig. 168 can be used in conjunc-
tion with a map if desired. Certainly a proposition carefully worked
208
MAP PRESENTATIONS
209
up and submitted, as was the
proposed bridge shown in Fig.
168, is more likely to receive
favorable consideration than
one in which only the ordi-
nary blue prints and maps are
used.
If maps must be printed
in a report, a book, or a maga-
zine, it is usually necessary,
on account of the high cost of
color printing, to use some
arrangement of black ink for
shading those areas which on
a single map would ordinarily
be colored by hand. Fig. 169
is a sample of what can be
done without the use of color.
If the drawing is made con-
siderably larger than the fin-
ished illustration, the shading
can be put on effectively by
hand work. Mechanical shad-
ing by the Ben Day process,
as regularly used by good en-
gravers, gives excellent results
but its use makes zinc cuts
rather expensive. Many illus-
trations in this book are made
by the Ben Day process. Any-
one wishing to know more
about the possibilities of this
process should look up Fig.
233 or consult the engraver
who is to make the line cuts.
Often the matter to be
presented calls for maps of
a large size, which can be
obtained only at considerable
210
GRAPHIC METHODS
Plateaus
Plains
Engineering Record
Fig. 169.
Drainage Area of the Canadian
River, New Mexico
Areas of different kinds may be distinguished on maps
by various classes of shading when color printing
is not available
expense. Sometimes only one
map is available when a variety
of plans must be presented.
In such cases, it is not feasible
to draw plans for new con-
struction work, or alternative
working schemes, on the map
itself. Most draughtsmen put
the map on a large drawing
board and then draw the new
constructions on separate sheets
of tracing cloth. The tracing
cloth is not very transparent,
however, and it will not help
greatly to get a project voted
upon favorably if the plan must
be presented to a board of direc-
tors on tracing-cloth drawings
with the map itself only very
dimly visible through the trac-
ing cloth. A much more effective scheme is to use a sheet of almost
transparent celluloid made with a rough surface that will take drawing
ink fairly well. The different alternative plans may then be drawn on
the celluloid in colored inks, and the different sheets of celluloid super-
imposed upon the map one by one as quickly as any executive com-
mittee or board considering the proposals may desire. The main
difficulty with the celluloid method is that the inks will rub off if the
celluloid is handled too much with moist hands. Ease of erasure has
some advantages, however, for tentative schemes can be rubbed out
or changed at will, simply by using a damp cloth. After the final
adoption of the plan, tracing cloth can be laid over the combined map
and celluloid sheet, and the important features of both may be traced
for blue-printing or for general reference later. Where maps must have
constant use, it is sometimes convenient to have them mounted be-
tween two sheets of clear celluloid. The celluloid-manufacturing com-
panies are prepared to do this kind of mounting to order.
Contrasts in map areas as shown in Fig. 170, by superimposing
one portion of the world on top of another portion, or by placing two
portions side by side on the same scale, are of considerable value.
MAP PRESENTATIONS
In geography books, and in other places where maps are most com-
monly seen, contrasted territories are frequently drawn to such dif-
ferent scales that a true idea of their proportions cannot be obtained.
The relative proportion can be indicated best when care is taken to
have the several areas drawn to the same scale and placed in a good
position for comparison.
Fig. 171 is shown here only as an example of the almost unlimited
range which the application of graphic methods may have. The av-
erage person would never think of charting a football game, yet £he
graphic method certainly gives the information more concisely than
could words alone.
Fig. 172 will be recognized by many readers as similar in general
scheme to the weather maps on which lines are drawn through all
points having the same temperature or the same barometric pressure.
Contour lines to show those points which are at the same height
above sea level give another application of the same general method.
Profile drawings similar to "Fig. 173 are commonly used by engi-
neers, but are not as well understood as they should be by others.
The main feature of the profile chart is the very great difference be-
tween the horizontal scale used to
mark distance and the vertical
scale showing the height of the
points represented. The vertical
scale of Fig. 173 should have been
shown on the chart. The heights
stated for different cities give a
fair indication of what the vertical
scale is and a reader can, if he
must, measure on the drawing the
height for any city and from that
determine to what scale the draw-
ing has been made. As a broad
rule, the scale should be indicated
in an easily seen position on every
chart, if the scale can be of assist-
World's Work i • i ii i
,,. HM- ^ c.- t ^ ance to any one besides the maker
Fig. 170. The Comparative Size of the
Philippines ol the chart.
By drawing the islands to scale and in solid black Considerable time and ingenU-
on a map of the eastern part of the United . , 1*1*
States, the relative size is clearly brought out ity may be USed in drawing Up a
GRAPHIC METHODS
-SECOND HALF-
>0 • 2S • 30 • JS~- *2O &S ce»rt* <pj-. <?o • 33 • 3O • 2S • 2O • JS • JO • S-
Boston Globe
Fig. 171. Second Half of the Harvard- Yale Football Game, November 23, 1912,
Final Score, Harvard 20, Yale o
The scale of the football field has been changed so as to give sufficient width for representing the plays by
lines and symbols of various kinds
MAP PRESENTATIONS
213
chart like Fig. 174 so that
the facts which it is desired
to prove may be brought
out clearly. Numerous
methods are available for
presenting such data.
There is no general rule for
determining which method
is the best, and judgment
must be used to choose the
method which is best fitted
to each individual case.
Note that in Fig. 174 we
have a scale reading to
quarters of a mile, and we
also have circles promi-
nently drawn on the map
at one-mile intervals to give
a clear idea of the distances
involved.
Country Gentleman
Fig. 172. Dates for Planting Corn, Showing How
the Season Advances in Different Parts of
the United States
This illustration is similar to the well-known weather maps on
which lines are drawn through all points where conditions
are the same
Though an illustration in the general method of Fig. 175 is at-
tractive, and will effectively gain the attention of the reader, the
method itself has all the inherent weakness of Fig. 36, Fig. 37 and Fig.
38 in Chapter III. If the reader wishes to practice some mental
gymnastics, he may try to work out the ratio between the number
of cattle in Idaho and the number of cattle in Texas. Though it
cannot be made certain, it is probable that the chart was drawn on
TSd — 655 — tSo — 335 — s66 4£0 400 35b 366
Railroad Operating Costs, Suffern & Son, New York
Fig. 173. Profile of the Pennsylvania Railroad from Jersey City to Chicago. The
Tabulated Figures Below the Profile Refer to the Spaces Between the Dotted
Lines
This is an example of a valuable method of presentation by which a horizontal scale much smaller than the
vertical scale is used so that great distances may be represented in a small space
214
GRAPHIC METHODS
an area basis. For the purpose of a visual and mental test, the area
basis may be used if Idaho and Texas are compared.
The method of Fig. 176 is now quite commonly used in Govern-
ment publications. This scheme for presenting data is not so striking
to the eye as that of Fig. 175, but it is more accurate. The scale given
with the map permits the number of cattle for any State to be read
fairly accurately. The degree of accuracy depends upon the map
size selected, and upon the number of dots used to represent any given
quantity. The more dots used the greater the accuracy. There is,
Graham Romeyn Taylor on "Satellite Cities" in the Survey
Fig. 174. Map Showing that Factory Workers of Norwood and
Oakley (Cincinnati) Live Long Distances from Their Work,
Many in the Heart of Cincinnati Rather than in the Sub-
urbs Near the Factories
The use of much heavier lines on the small circles and the figures in them would
have improved this chart. Pins or black-ink dots, each representing say 20
workers, would give a good result by using the method of Fig. 198
however, a limit to the number of dots which may be used, or the dots
will of necessity be so small in diameter that the quarter circles will
be impossible for the eye to distinguish. In Fig. 176 it would not
be feasible to use a much smaller circle if the quarter-circles are used.
MAP PRESENTATIONS
215
Country Gentleman
Fig- I75- Relative Distribution in the United States of Cattle Other than Dairy Cows
For popular presentation, if great accuracy is unimportant, this method of illustration would be difficult to
improve upon. It is not possible to get a correct comparison between any two States because any one
circle cannot be fitted visually into the area of another circle. Compare the method used in Fig. 176
• 400,000 cattle.
9 150,000 to 200,000 cattle.
O 100,000 to 150,000 cattle.
O 60,000 to 100,000 cattle.
O Leas than 50,000 cattle.
The heavy liaea (•») show geographic divisions.
Abstract of the Thirteenth Census of the United States, 1910
Fig. 176. All Cattle on Farms in the United States, by States, April 15, 1910
Here a definite scale is given which permits fairly accurate reading of the number of cattle for any State.
The visual contrast between States is also quite striking. Though not so clear-cut as Fig. 175, this
illustration ha.s more accuracy
216
GRAPHIC METHODS
In making up copy for the line cut of Fig. 177 very little hand work
was required. If an outline map of suitable size is available, the only
hand work necessary for a cut of this kind is in drawing the small
circles and placing inside them the figures serving as key numbers
for the shading used. The actual shading is done by the engraver
making use of the Ben Day process. For information regarding the
preparation of engraver's copy for plates on which Ben Day shading
is desired, see Fig. 233.
HORSE POWER
7.OOO.OOO — S.OOO.OOO
4,000,000 —
7.OOO.OOO
2,000,000 —
4,000,000
i.ooo.ooo —
2,000,000
500,000 —
I.OOO.OOO
25O.OOO —
5OO.OOO
1OO.OOO —
250,000
50.OOO —
1OO.OOO
f> I LESS THAN I5.OOO
Fig. 177. Potential Water Power in the Different States of the United States
This is a splendid example of the contrasts in shading made possible by the Ben Day mechanical processes
of engraving. Nine contrasting shades increasing in darkness are used here with absolute distinctness.
The small number in the circle used to identify the shading is of great advantage
There is one serious error which should be avoided in the inter-
pretation of any shaded map like Fig. 177. The key scale at the
lower left-hand corner of the illustration shows that the different
shades do not become darker by any uniform increase in horse power.
The range included in shade number eight is 50,000 — from 50,000
to 100,000. For shading number two, however, the range is 3,000,000—
from 4,000,000 to 7,000,000. This numerical scale was badly selected,
for the steps vary so greatly in size that the increasing degrees of shad-
MAP PRESENTATIONS
217
Less -than SO bushels per acre.
2O to 4O
4O bushels per acre, and over.
Fig. 178. Yield of Corn per Acre in the Eastern Part of the United States in 1900
Here the data have been recorded by counties rather than by States. This chart is an example of what
any draftsman may do by hand shading. It would have been better to use the smaller numbers to rep-
resent the best rank, as was done in Fig. 177
218
MAP PRESENTATIONS . 219
ing, as they appear to the eye, mean practically nothing. States having
shading number two could vary from each other in the amount of
horse power by more than the whole quantity of power in States
having shadings from three to nine inclusive. If the steps in the
shading scale had been so made that there were nine increasing classes
of shading, each representing 1,000,000 horse power, it can be seen
that all the States here numbered five to nine inclusively would have
the same shading. Such a map made with a scale of uniform steps
would appear so entirely different from the map shown here that no
one would ever recognize the maps to have been made from the same
data. The selection of scale for maps of this kind is important in order
that the map may tell a truthful story. Wherever feasible, the nu-
merical scale intervals for colorings or shadings should be uniform.
Frequently the data are of such kind that there is much concen-
tration at some portion of the scale, but with important facts to show
at other portions of the scale above and below the point of greatest
concentration. It may then be desirable to use uniform scale-steps
for the shading in the portion of the scale with greatest concentra-
tion, and to have smaller scale-steps at either end or at both ends of
the scale. In Fig. 177 small scale-steps would seem desirable for the
lower portion of the scale.
It will be noticed in Fig. 177 that the numbers denoting the shadings
are arranged with the smallest numbers to represent the largest quanti-
ties. This arrangement was made purposely. On a map of the kind
seen in Fig. 177 there may be any number of different shadings, from
one to a dozen or more. In order to simplify matters for the reader it
seems best to assign the smaller numbers to represent those conditions
which are considered most desirable or commendable. The reader may
then see instantly which areas are first, second, third, etc., in rank
simply by observing the figures inside the small circles.
In Fig. 178, if it be assumed that there is a likelihood of corn crops
going up to 60 bushels per acre, the scale intervals are shown as uniform.
Fig. 178 is of interest chiefly because it shows what can be done by hand
ruling when it is necessary to produce an illustration for a report in
which an expensive cut by the Ben Day method cannot be justified.
Fig. 179 does not do justice to the possibilities of the Ben Day
method of shading. The cut was made by photographing a page of the
Census Abstract which was printed on rather rough paper. With an
original cut made directly by the Ben Day process the distinction
220
GRAPHIC METHODS
between the different shades would be considerably clearer than it is
in Fig. 179. A cut of this size and complexity is rather expensive
when the Ben Day shading is used. Anyone wishing a cut made with
Ben Day work would do well to get a rough cost-estimate from his
engraver before actually giving the order.
It will be noticed in Fig. 179 that the numerical scale-steps for
different degrees of shading are uniform except at the smaller end of
the scale. It would probably not be wise to show as white area all
of the land valued at from $10 to $25 an acre, since such land makes
Nomta
de maison*
*
Bertillon's "Course elementalre de Stalistique Administrative"
Fig. 180. Height of the Houses in the Different Districts of Paris
The scale for this illustration should have been indicated on the chart so that actual numbers of houses
could be read. The vertical dimension of the group of bars for each district shows the relative total num-
ber of houses. The horizontal dimension shows the relative number of houses of each height by stories
up about half of the whole United States. A uniform scale varying
by $25 per acre would give an erroneous impression regarding those
important areas which contain land valued at less than $25 per acre
but in which there is a large amount of farming.
Map diagrams of the type shown in Fig. 180 are sometimes useful.
There is danger, however, of making a chart of this kind so popular
in character that it loses in accuracy. The utility of Fig. 180 is at once
MAP PRESENTATIONS
POPULATION DENSITY PER ACRE:
O-50
50-75
75-10O
100-150
I5O-EOO 8OO-E50
a5O-3OO 3OO-35O 35O-4OO 4OO-45O Over45O
Courtesy of Graham Romeyn Taylor
Fig. 181. Methods of Marking Maps When an Increased Density of Population
May be Expected in Following Years
Each shading can be made by adding with a pen to the shading used for the next lower density. Pins of
different colors placed in a map have an advantage over this scheme in that pins can be removed if
population density should happen to decrease
limited by the fact that there is no key scale shown from which an
exact numerical interpretation may be obtained.
The scheme for indicating population density shown in Fig. 181
is necessary only when very large and valuable maps are used. For
ordinary purposes it would be better to have a new map for each Census,
and then to use colored crayons on the different areas of the map,
rather than to attempt the complicated scheme of Fig. 181. If, how-
ever, a photograph must be taken periodically to produce line cuts
showing the map in printed form on a reduced scale, colored crayons
cannot be used and the scheme of Fig. 181 may be of great assistance.
The result obtained by the method of Fig. 181 may be obtained by using
map pins with spherical heads and pushing the pins in until the heads
touch the map. The number of pins in any city block or district would
indicate the population according to some simple scale. If it is not
necessary to photograph the map, pins with different colors of heads
may be used to show density of population. There is one very great
advantage in using pins instead of crayons or the pen-and-ink system
of Fig. 181. It sometimes happens that an error is made which may
spoil a very valuable map because of the impossibility of erasure. When
short pins are used instead of crayon or ink, an error can be instantly
222
GRAPHIC METHODS
NEW ROADS WHICH
» 50.000. 000 BOND ISSUE
— -— ROADS BUILT BEFORE THE
DIX ADMINISTRATION
«...«.. ROADS TO BE BUILT UNDER SECOND
^> 5O,OOO,OOO BOND ISSUE
Wm. Pierrepont White, of Uttca, N. Y.. in the New York Times
Fig. 182. Map Showing 3,500 Miles of Completed and Proposed State Roads, in
New York's Proposed i2,ooo-Mile System. The Shaded Portion Shows a
Strip Ten Miles Wide which Contains 90 Per Cent of the Taxable Valuation and
80 Per Cent of the Population
The object of the illustration is to show the necessity of a road system that will feed from the farms to the
densely settled portion, permit the quick and easy transportation of farm products to the cities, lessen
the cost of living, and thus justify the taxing of the State as a whole for the construction of this system
corrected by pulling out pins. Also, if there should be a reduction in
the density of the population, pins can be pulled out, whereas with the
pen-and-ink method of Fig. 181 it is not possible to proceed backward
on the scale of marking and a decrease can never be shown without
making another map or marring the old one.
In Fig. 182 is seen a good example of the graphic method applied
to newspaper writing designed to convince the reader by specific
argument. The presentation is very effective. The shaded portion
of the map shows a strip which contains 90 per cent of the taxable
valuations and 80 per cent of the population. The possibilities for the
use of maps in arguments of political or economic nature are almost
MAP PRESENTATIONS
without limit. It is rather surprising that maps for such purposes
have not been more generally employed.
Though the map record sheet shown in Fig. 183 may appeal to
some business men, there would seem to be little advantage in that type
of sheet over tabulated figures in a column. The column arrangement
would have a desirable feature in that different entries could more
easily be compared for size by judging the number of digits contained
in each entry.
The method shown in Fig. 184 can be widely used in map problems
relating to any kind of travel over specific routes. In this particular
case the map concerns the movement of freight. Maps of this type
are very commonly used to show the number of passengers carried on
different city transit lines. To make an illustration on the plan of
Fig. 184, the width of each broad strip is carefully drawn to some scale
representing the total quantity movement. A map like this is easily
drawn yet it is very effective, particularly if colors are used for the broad
strips while the route itself is marked by means of a black line in the
center.
"
By Permission of "System"
Fig. 183. Blank for Recording Sales to Consumers and to Dealers, Abbreviated
by the Letters "C" and "D" for Each State
A blank like this can be filled out daily, weekly, or monthly as desired
224
GRAPHIC METHODS
Maps on the scheme of Fig. 184 are made entirely in the plane of
the paper itself. In Fig. 185 we have a map presentation in which
quantities are represented by building vertically above the various
routes laid out on the map. For the map of Fig. 185, the vertical
representation was made by strips of wood, alternately black and white,
glued carefully above each one of the street-car routes. Each of the
strips of wood represents 4,000 passengers carried on the street-car lines
in 24 hours. The model gives the whole transit situation with sur-
prisingly great clearness, and a better presentation than this could
scarcely be imagined.
KANSAS cnr
AMRO
QUAHAH
Railway Age Gazette
Fig. 184. Map Diagram Showing Freight-traffic Density and Direction on the St.
Louis and San Francisco Railroad for the Fiscal Year 1912-13
The figures are in terms of 100,000 net tons hauled one mile per mile of road.
A map of this kind is easily made and is often of very great utility. The method can also be used to show
the number of passengers carried on railroad, subway, or street-car lines, etc. Compare Fig. 185
The method used in the construction of the model shown in Fig. 185
gives magnificent results, but wooden strips are not practicable except
on a very spacious map. The wood-strip method also involves a large
amount of time on the part of a skilled workman, and workmen to
Courtesy of Dr. Ewerbeck. Internationale Baufach-Ausslellimg, Leipzig, Germany, 1913
Fig. 185. Passengers Carried in Twenty-four Hours on the Street-car Lines of
Frankfurt a M., Germany. Each Vertical Strip Represents 4,000 Passengers
The map is about eight feet square. Strips of wood are glued above each street having a car line. This
is an excellent presentation of facts
225
226 GRAPHIC METHODS
do this class of work are not so easily found in the United States as
in Germany.
An excellent map of this general type can be made by using sheet
metal, as aluminum or zinc, ruled or painted with lines or colored
stripes representing the vertical scale to which the information is to be
shown. Where two transit lines intersect the strips of metal can be
riveted or soldered together. As aluminum is not easily soldered it is
best to use zinc or tinned iron if solder is to be the means of holding the
vertical strips to each other. In many cases solder is unnecessary, for
the strips may be held vertically by notching each strip halfway through
so that the strips can be interlocked in the manner shown in Fig. 236.
By using sheet metal a much cheaper construction can be obtained than
by wood strips. The sheet-metal method also permits the use of a
map of much smaller size and finer scale than would be feasible if wood
strips were the means of obtaining the necessary vertical height.
CHAPTER XII
MAPS AND PINS
PIN MAPS have not been much used in the past, chiefly because
a map pin which would give satisfactory service has not been
available for common use. Until recently the map markers
obtainable have been little more than old-fashioned carpet tacks having
chisel-shaped points which cut the surface of any map into which they
were pushed. Tacks with rough steel shanks cannot be pushed far
into a map if the tacks are to be pulled out again. Also, rough steel is
likely to rust so as to cause the whole tack to deteriorate rapidly.
Cloth heads on the map tacks make it possible to have tacks in dis-
tinct colors and plaids. The cloth tops, however, fade in the sunlight
and collect dust so that in a short time the different colors of tacks on
any map, exposed as a wall map must be, cannot be easily distinguished.
The crudeness of the cloth-covered tack makes it unsatisfactory for
many kinds of map work. Cloth-covered tacks are long, and long tacks
which can be pushed only a short distance into the surface of a map are
not satisfactory, for they are likely to drop out or be knocked off by
any slight disturbance.
Wall maps with long projecting tacks are not practical for office
use unless protected by an expensive frame with a glass cover. As it
is usually necessary to open up such a glass map-case to change the
position of the tacks frequently, the construction of the case becomes
unduly expensive. Without a glass cover a wall map with long pro-
jecting tacks is likely to be damaged by the feather duster of the janitor.
Even when maps with long projecting tacks are safeguarded by
being placed in separate drawers of a cabinet made for that purpose,
there is still a probability that some of the tacks will come loose from
the mounting and rattle around inside of the map drawers. This is
a point not realized by most men who install map and tack systems,
but it usually sooner or later sounds the death -knell of the tack system.
227
GRAPHIC METHODS
Generally the tacks are placed in the maps one by one as agencies are
established or as data are obtained from correspondence. After the
correspondence by which each tack was located has gone to the cor-
respondence files, there is ordinarily no list showing the geographical
location of the tacks. If a single tack is found loose in the bottom of
a drawer of a cabinet system, or on
I the floor of an office where there is a
£jk wall map, it causes distrust of the
• i . vT. • • • -T^ whole tack installation. When
there is no list showing the geo-
graphical location of different
Fig. 186. A Contrast Between Long, tacks, the one tack which is
Cloth-covered Map Tacks which are . <? i . i , i i
Likely to Fall Out, and Glass-head out of Place cannot be Put back
Map Phis Made with Short Needle- without checking over corre-
points. so .thatthe Pins May be Pushed spOndence and records which
in until the Heads Touch the Map , , , „ -„
may extend back tor years. Lven
when a list of tack locations is at hand, the loose tack cannot be replaced
without checking the location of all the tacks on the map one by one
to determine by a process of elimination where the loose tack came from.
In the ordinary course of human events it is not likely that a tack falling
out of a map would be found to give warning that the map record is
no longer accurate. The tack system using long projecting tacks may
therefore contain unsuspected inaccuracies just because tacks may have
come loose. The unpleasant suspicion that a map record may be inac-
curate, because of the long tacks falling out, sometimes causes a man to
abandon the tack system entirely, believing that it is not reliable
enough to give data on which important decisions must be based.
Map and pin systems are of such tremendous assistance that they
should not be condemned simply because the map pin itself has not
been satisfactory. By using a short pin with a needle point and by
having a backing for the map such that the needle point can be pushed
in until the spherical head touches the map, we can secure a map
system which is absolutely trustworthy. Since the pin is pushed in to
its full length, a blow cannot dislodge it. The spherical head in contact
with the map gives a very neat appearance, yet the spherical shape per-
mits the fingers to remove the pin by straight pulling without any diffi-
culty whatever. The smooth needle-point of good quality steel does not
rust easily and it does not cut the surface of the map. When a pin
must be removed, the hole is so small that it is scarcely noticeable.
MAPS AND PINS
Pins having spherical glass heads may be used on wall maps with-
out any danger of the heads fading from sunlight. The glass surface
is so smooth that dust cannot collect sufficiently to affect the color
appearance of the pin head. Even if the map does get dusty, it is
perfectly safe to use the feather duster on a wall map having pins which
are pushed in so far that the spherical heads are in contact with the
map surface. Dusting of such a map will not loosen the pins in any
Fig. 187. Location of the Plants Affiliated with the University of Cincinnati, College
of Engineering. Every Star Represents a Plant Where Co-operative Engineer-
ing Students are Employed
A wall exhibit like this is easily made by using a red legal seal and red stars such as can be purchased at
many good stationery stores
way. A wall map on which pins with spherical glass heads are used can
be very cheaply mounted, it needs no glass cover, and the pins can be
put in or taken out instantly, thus giving a location record which is at
all times in plain view, yet thoroughly accurate.
Another great advantage of the pins with spherical glass heads is
that they may be obtained with small-diameter heads, which permit
the use of numerous pins on maps of small size. In portraying many
230 GRAPHIC METHODS
classes of information, it is impracticable to use the cloth-head tacks
because the heads are so large that the tacks touch each other in all
thickly populated regions.
Photographs taken of a map containing tall pins or tacks give an
inaccurate effect, since the angle of the lens causes the head of the
tack to appear at one side of the point in which the tack itself is lo-
cated. Thus, in a photograph of a map of the United States the head
of a long pin or tack set at Providence, R. I., might well show near
Boston, Mass. There is no way of avoiding this error if projecting
pins and tacks are used. The only safe plan is to use the spherical pin
head which is in contact with the map surface itself. Photographic
views of a sphere are the same from all directions, thus causing all
pins to appear exactly the same size and shape on the photograph.
Photographs taken of a large map with flat-headed tacks show the
heads in the center of the picture as circles, while the heads towards
the edge of the picture look of much smaller size, because they appear
flattened out as ellipses. The visual effect for points toward the edge
of the map is lessened when the tacks are flat headed, and an un-
necessary visual error is brought into the picture.
A very cheap yet satisfactory mounting for a wall map to be used
with glass-head map pins is made with three or more layers of corru-
gated straw-board. The straw-board used should be about 3/ie-mch
thick with a facing on either side of the corrugated portion. Three
thicknesses of straw-board are sufficient to give strength for any map
up to one yard long. The two outside layers of straw-board should
be so arranged that the corrugations will run with the length of the
map, thus giving the greater strength in that direction. The middle
layer should have the ribs running crosswise of the map so that the
map mounting will be safeguarded from bending in either of the two
different directions. Where very large wall maps are desired, six or
more layers of straw-board may be used to give sufficient strength. If
single sheets of straw-board cannot be found as large as the map
itself, the map mounting can easily be built up of small sheets of
straw-board, provided the joints in the straw-board are so placed
that they will not be over each other to weaken the finished structure.
The straw-board backing for a map to be used with pins is not
the best obtainable if the pins must be put in and taken out frequently.
When, however, the pins are to be placed in the map and left there,
the straw-board is just as satisfactory as any other backing for a
MAPS AND PINS . 231
map. A layer of the cheapest kind of muslin placed over the face of
the straw-board will prevent the pins from tearing the surface of the
map if they happen not to be pushed in exactly straight. The use of
cloth over the straw-board also permits of changing the pins many more
times than would be feasible with straw-board without the cloth
reinforcing.
Review of Reviews
Fig. 188. Every Phi Dot on this Map Marks the Home of a Student of the University
of Cincinnati
By using a map printed in colors which do not photograph as black, the pins show up distinctly on the map
as a background
Before mounting a map the colors should be tested to make sure
that they will not run in water. The map should then be wet all
over, preferably by laying it flat for a time in a large tray. Use a
flour-and-water starch paste, paper-hanger's paste, or library paste
of the kind used in mounting photographic prints. Carefully remove
GRAPHIC METHODS
all wrinkles and press the excess paste out from under the edge of
the map. Shrinkage of the map and of the moistened straw-board
surface will almost certainly cause the straw-board mounting to warp
unless care is taken to prevent warping. At the same time the map
is pasted on the front of the straw-board, paste a sheet of wet wrapping
paper on the back of the straw-board mount. The shrinkage of the
wrapping paper on the back will equalize the shrinkage of the map
on the front of the mount. Place the mounted map on a flat table
surface or on a smooth floor, and stack books or other heavy articles
upon the mount over night or until thoroughly dry so that any ten-
dency to warp in the drying may be overcome by the weights.
Finish the four edges of the corrugated straw-board by using
gummed cloth tape or paper tape neatly folded over the edges in the
manner ordinarily used with passe-partout pictures. To hang up the
finished map use two com-
bination clamps and rings
such as may sometimes be
obtained in stores selling
window shades. These
metal-clamp fixtures are of
neat appearance and of
strength sufficient to hold
a map of any size. If two
nails or hooks are used in
the wall to support the
map, the ring hangers allow
the map to be instantly re-
moved to a desk when addi-
tional pins must be put in.
If pins are to be put in and taken out of a map repeatedly, it
should be mounted on good quality cork composition. Exhibition-
board, compo-board, wall-board, or any of the various boards gener-
ally used for wall surfaces may be used as a backing to give strength
to the cork. Care should be taken to get a good quality of board
which will not warp seriously. The cork composition can be glued
to the wall-board and then the map pasted on the cork. A piece
of wrapping paper should be pasted on the back of the wall-board
at the time the map is mounted so that the shrinkage of the map
may be equalized. The edge of the cork mounting may be bound
Country Gentleman
Fig. 189. Distribution of the Field Service of
the Department of Agriculture, February i,
1912
A pin map cannot be excelled for conveying information like
this. Note the great activity of the Agricultural Depart-
ment in the South
MAPS AND PINS
233
Thomas G. Plant & Co., Queen Quality Shoes
Fig. 190. The Use of Pin Maps in Advertising
A large shoe manufacturing company used this illustration in an advertisement announcing that 3,800
merchants were ready to show the latest fall and winter models of shoes
In order to make the dots stand out distinctly it would appear that agencies in any State have been shown
as uniformly distributed over the State. Actual exact locations would be almost impossible to show
unless a much larger map were used
with a cloth tape as suggested for straw-board mounts, or the whole
built up combination may be framed with picture framing but without
using any glass covering. The cork composition used should be 3/s-inch
thick. Maps backed with cork composition and used with glass-head
pins having needle points will permit almost unlimited puncturing
from frequently moved pins. If the map is mounted on cork composition
the sharp-pointed pins are easily pushed in and removed, yet the record
is always accurate because the pins cannot be knocked out.
Numerous wall maps can be very conveniently used if they are
mounted on vertical swinging-leaf display fixtures similar to those
shown in Fig. 219. The two surfaces of each swinging leaf should be
covered with corrugated straw-board and muslin, or preferably with
cork composition in order to get a good surface into which to insert
the pins. As adjacent leaves are likely to strike and break the glass
heads of the pins, projecting bumpers should be placed on every
other leaf to allow enough clearance for opposite pins when the leaves
come in contact. The rubber-covered bumpers used to prevent door
234 GRAPHIC METHODS
knobs from striking plastered walls can be placed at the top or bottom
of alternate leaf surfaces. If these rubber bumpers are not available,
a narrow strip of wood at the top and bottom of each leaf will serve.
When employed with glass-head pins having needle points, the
drawer cabinets for maps used to route salesman, etc., can have a
•layer of cork composition fastened in the bottom of each drawer.
The maps are then glued to the surface of the cork composition. The
drawer cabinets regularly found on the market have sufficient drawer
depth to permit placing a ^g-inch layer of cork composition in the
bottom of each of the regular drawers and still allow room for the
pins. Map pins may be pushed into the cork composition so se-
curely that no pin will ever be misplaced even if a book or other heavy
object should happen to drop upon the map and the map pins. Pins
in cork composition are so easily inserted and removed that they can
be handled more rapidly than if stuck into any kind of a board sur-
face. When ordering maps from any map manufacturer or map store
for use with glass-head pins care must be taken to specify either a
cork-composition backing or a corrugated straw-board backing, else
the map will probably be shipped mounted on compo-board or some
other surface entirely too dense to permit of pushing the map pins
in until the heads touch the surface of the map.
If numerous glass-head pins are to be put into a map at one time,
the eraser in the end of a lead-pencil should be used to push the pins
down until the heads touch the map. Pins can be very quickly lo-
cated if only their points are pushed into the map by hand, leaving
the main pressure to be applied by the lead-pencil eraser after a num-
ber of pins have been located. The pencil-eraser method saves time
and it also eliminates the discomfort which may be caused if thousands
of pins are pushed into a map by using the thumb and forefinger only.
Line cuts, sometimes called zinc cuts, may be made directly from
pin maps if glass-head map pins of suitable color are used. At the
point on the map where each pin head is located there will be a black
dot on the print made from the zinc cut. As light is reflected from
the surface of the glass heads of the pins, there are sometimes shown
in a photograph high lights which must be retouched with a pen or
a fine brush so that the whole spot shall be black, rather than black
with a white center, as seen in Fig. 191. Anybody can do this re-
touching very quickly. It is mentioned here only as a caution that
the photograph be inspected before the zinc engraving is made from it.
MAPS AND PINS 235
Photographs for line cuts must have a good contrast of white and
black, or colors which photograph as black. Photographs or original
drawings containing shades of gray will not produce good line cuts
and frequently cannot be used at all for the zinc engraving process.
When line cuts are to be made from pin maps it is best to be certain
that the glass-head pins are selected in colors which will photograph
as black. Red, orange, and black pins can be used without any ques-
tion, since negatives made from these colors give a dead black on
the photographic print. Line cuts can also be made from dark green
and some of the other colors. Where it is necessary to make photo-
graphs and line cuts from a very expensive and elaborate pin map,
it is wise to consult the engraver before the pin colors for the map are
finally decided upon. The color blue should be carefully avoided if
photographs or line cuts are to be made, since blue almost totally fails
to show up on a photograph.
If half-tone engravings can be used to illustrate the pin map,
many more different colors of pins may be used on the original map than
when zinc cuts are the means of printing. Another advantage of
half-tones is that different colors of pin heads are represented in the
half-tone by different shades of gray, as can be seen in Fig.. 191. On
the left half of Fig. 191, fourteen different colors of glass-head map
pins were used. The photograph was not retouched in any way.
Fig. 191 thus represents about what can be expected of different
colored pin heads for contrast in half-tone illustration. Note the
high lights which give white spots on the circles of the darker pin heads.
It is spots like these which should be retouched by hand on any photo-
graph from which a line cut is to be made.
Tacks and pins have been used on maps to locate agencies, sales-
men, customers, etc., more than for any other one purpose. The
various possibilities in applying tacks and pins to sales-department
work cannot be thoroughly covered here, but if a few general methods
are known, each sales manager can work out for himself the pin scheme
which best suits his own conditions.
Fig. 191 was photographed, without any retouching, direct from
a section of the United States Geological Survey topographical maps.
These contour maps, having a scale of about one inch to the mile,
may be obtained from the Geological Survey at Washington, for most
of these sections of the country which are thickly settled. The maps
are very low in cost and yet are remarkably accurate. Fig. 191 was
236
GRAPHIC METHODS
MAPS AND PINS 237
purposely photographed at an angle of about 45 degrees. As the
upper part of the illustration is out of focus because of the angle,
the illustration does not do justice to the Government maps. Another
reason why the map does not come out clearly is that brown ink is
used to print the contour lines and these lines accordingly show only
faintly in the half-tone.
When it is necessary to show the routing to various points on a
map the best method is to use a fine red string or thread between
map pins as seen in Fig. 191. If the routing must be changed the
thread can be almost instantly moved to connect the pins in some
new order. Lines could be drawn on a map in ink to show routing,
but the map would be ruined if any change in routing should ever be
necessary.
In the preparation of illustrations for reports, advertising, etc.,
whether maps with or without pins are used, great care must be taken
in the selection of the map itself. Map manufacturers have a very
annoying custom of purposely making maps in such manner that the
maps cannot easily be duplicated by photographic processes. Maps
printed in blue ink are almost hopeless for use in making zinc cuts.
Maps on which large areas as States, or counties, are differentiated by
the use of colors red, orange, green, etc., do not produce either good
line cuts or good half-tones since the colored areas on the original maps
are likely to show as solid black areas and blot out all detail on the
photograph. If an illustration must be made from a map it is well to
be sure that the map is printed in black, red, or orange outline so that
the resulting photograph will have distinct contrast. Maps should
contain as little detail as practicable, to make certain that the pin heads
or other representations of specific data will show up as distinctly as
possible. Fig. 192 is a good example of the kind of map to use for
reproduction when pins are employed. Notice in Fig. 192 a heavy
border for the country as a whole, and the outlines for each State.
Towns and rivers are not shown. Each dot on the map may thus be
seen with great clearness.
As maps are very carefully copyrighted by most map publishers,
maps which are copyrighted should not be reproduced without con-
sideration of the copyright. For maps which are photographed down
with comparatively little change, permission should be requested from
the map publisher, to make certain that unpleasant complications such
as damage suits or the holding up of a publication may be avoided.
238
GRAPHIC METHODS
The 228 Principal Trading Centers
Saturday Evening Post, Curtis Publishing Co.
Fig. 192. The 228 Principal Trading Centers in the United States
This illustration was taken from an advertisement proclaiming that a certain magazine's circulation was
mainly in the 228 chief trading centers of the country, and that, accordingly, the magazine must be
effective as an advertising medium for merchandise
Note that in the east the dots are so numerous they are shown as crescents. The crescent scheme is a good
one as it permits the use of a much larger dot than would otherwise be possible
The amount of detail which may be permitted on any map in which
pins are used depends on the size of the resulting illustration and the
size of the pin heads. If the pins are so numerous that the map must
be very large, there is danger of reducing the map so much in size be-
tween photograph and final illustration that the pin heads will appear as
indistinct dots on the complex surface of the map. In Fig. 193 a map
was used in which there was more detail than really necessary or desir-
able for a clear illustration. In justice to the General Electric Review it
must, however, be said that the map shown in Fig. 193 has been reduced
in size and made smaller than it was in the original print. This map
could not be reduced further without danger of completely losing the
pin heads in the gray background resulting from so many lines on the
map.
In producing an illustration like Fig. 193 considerable ingenuity
must be used to make two or more classes of pins show out distinctly
in zinc cuts which can be printed in only one color. The pins on the
OF 1000 HP. AND OVER
AND
POWER
SECTIONS OF STREAMS
IN THE
O F
Commercial Dere/opmenfs
Manufacturing Developments
ine i'v~-) for Stream, indicates
qhly*SectJon having power.
* '* yr
General Electric Review
Fig. 193. Location of Water-Power Developments of 1,000 Horse Power, and Over,
and Power Sections of Streams in the United States
The original of this map would have pins in two different colors. The photograph taken from the map
would be retouched by the use of a pen so that squares would replace dots for one of the two colors
of pins. The illustration shows a contrast of dots of two shapes rather than dots of two colors
239
240
GRAPHIC METHODS
,1 IP
"if PpB^
^W%';^%.:"^
o
a
O
t
O
b ;/s
s M
I "ft
$2
.a
=•5
a
^*
o
i
*->
o
rt
a <u s
p fp i
«3 ^
la IS
•532o,
<L> '
rt S
t! ^
^
o<'
CD
>5
W^
0.23
1
j^
CO
•S
.5
o
i 1
3
r I
PS* H
MAPS AND PINS
original map can be in different colors. After a photograph has been
made of the pin map it is best to compare the photograph with the
original, and then to make squares out of those circles which represent
a certain color of pin on the original map. Squares are easily made by
using a fine pen on a photograph considerably larger than the cut itself
will be. When the final dots are not too small in size it is possible to
make shapes with the pen such as triangles, outline circles, etc., which
can be distinguished from one another.
If a great reduction in size is necessary between the original material
and the finished illustration, extreme care must be used to have all
the lines on any original drawing wide enough to stand the reduction
in line thickness due to the decrease in size. If a drawing one foot
wide is photographed down to an illustration three inches wide the
lines will be only one-quarter as thick as in the original drawing. Lines
on the original drawing must therefore be made very wide — in fact,
much wider than is ordinarily considered desirable until experience has
been gained from several disappointments in the appearance of finished
illustrations. It is not easy to find maps with lines sufficiently heavy
to permit of the great photographic reduction usually necessary in
making illustrations from pin maps or other map representations.
Quite often it is necessary for the person making a map chart to go
over by hand all outlines such as borders and the divisions between
States, counties, etc., to make those particular lines very much heavier
than on any map which can be purchased.
A reducing glass which makes everything seen through it appear
smaller is almost essential when many maps or charts must be repro-
duced. A convenient size of reducing glass has a single lens, about
1^4 inches in diameter, and causes objects to appear from one-half to
one-quarter the size of the original. The amount of reduction can be
varied by holding the glass at different distances from the original
drawing. In order to tell how much reduction in size is made by the
glass at any given distance, it is possible to look at the original object
with one eye and through the reducing glass with the other eye so that
by superimposing the two images their length may be compared. When
a chart has ruled lines, as co-ordinate lines, it is a simple matter to
superimpose the images from the two eyes so that one square of the
original equals two, three, or four squares of the image seen through the
reducing glass. When the two images are thus superimposed, study
can be made of the thickness of lines or other details in the reduced
242 GRAPHIC METHODS
size so that a decision may be had as to whether the drawing will safely
stand the proposed reduction without having the lines made heavier.
Fig. 194 shows about the extreme limit of what can be done in the
making of pin maps. The original map here was 40 inches wide and
66 inches long. Nevertheless, the map shows up satisfactorily in the
greatly reduced size of the half-tone because care was taken to have
very wide lines and little detail on the original map. Each of the 19,500
pins of five different colors.had a head diameter of 3/32 inch. It must be
remembered, that most of these pins were in the characteristic blue
colors commonly associated with the Bell Telephone System, and,
because blue is almost impossible to photograph, the pins do not show
out as strikingly as they would if other colors were used. The black
splotches on the map were caused by the predominance in those areas
of pins with dark blue heads. When this pin map was made there was
no intention of taking a photograph of it. A much more distinct
photograph would have been secured if pins in the contrasting colors
of red, orange, black, green, purple, etc., had been chosen. All of these
would have shown dark in the photograph, instead of white or light
gray like the pale blue pins which in Fig. 194 were used in the greatest
number.
Fig. 194 was photographed at an angle. The eastern half of the
United States appears smaller than true scale because of the perspective
in the picture. The perspective view shows that the glass-head pins
had long shanks. This map, costing several hundred dollars to pro-
duce, could be injured severely by a few strokes of a janitor's feather
duster. If short pins were used with spherical heads in contact with
the map there would be no danger of the pins being misplaced. An-
other disadvantage of the long steel pins is that the steel portion exposed
to the atmosphere is likely to rust, especially in cities near salt water.
Pins with short needle-points pushed entirely into cork composition
or corrugated straw -board have little opportunity to rust.
Fig. 195 shows a convenient map scheme by which different places
on the map are numbered so that detailed information regarding each
may be obtained from the annexed tabulation numbered to correspond
with the pin numbers. In this scheme we have all the advantages of
a pin map without the confusion of too many data on the surface of the
map itself. The illustration of Fig. 195 was evidently prepared by
hand. Such an illustration can, however, be made by using pins like
those shown in Fig. 196, or like pin No. 20 in Fig. 199. This latter
MAPS AND PINS
243
No.
1 Gum FALLS FORT. CEM. Co
S. HILDERBERO CEM. Co
3. ALSIN'S AM. PORT. CEM. WORKS
4- HUDSON PORT. CIM. Co
5. Earna PORT. CEK. Co
...Ota»Fau«.N.Y.
. . . How* Can, N. Y
. . . Aben, N. Y
. . . Huown, N. Y
...WaramwN.V:
. . . Portland Point, N. Y
ft. ft.
D.4H.R.R....
D.4H.R.R....
N. Y. C. 4H. R.
N. Y. C. 4H. R..
N.Y.C.4H.R..
L.V.R. R
ID. L.4W. 1
)ErieR.R...f
N.Y.C
Penn. R, R
P.4R
P.4L.E
N. Y. C. 4 H. R
Cap. Bbb,
per day
1.800
2000
4300
""woo
500
600
VbO
2500
2300
1,200
3500
1500
2300
•27,000
•36,600
3,600
1500
1500
2.000
•36.600
1,200
1500
1500
•27.000
•36.600
2.000
1500
3300
3,000
4.000
1.200
1.200
2,000
2.000
1000
tcago
7. WATLAND POST. CEM. Co
8. MARENOO PORT. Cm. Co
...WaylamLN.Y
. . . Caledonia, N. Y
9. VrNDEX PORT. CEM. Co
10- ALLENTOWN PORT. CIM. Co
. . . Molltown, Pa ,
. . . Evanrvrille, Pa
New Castle, Pa
12. CATSKILI CEK. Co
... Cementon, N. Y.. .
13. JAMESTOWN PORT. CEM. Co
14- SANDUSKY PORT. CEM. Co
... Yorktown, Pa
.York, Pa
Penn.R.R
15- SECURITY CEMENT A LIME Co
... Security, Md
WeatHd7R.R..
Penn. R. R
P.4L.E..
P.4L.E
......B.&Q. &.&....
Penn.R.R
L. S. 4M. S
.....C.H. V.4T....
C.H. V.4T
N 4W
L.S.4 M.S..:.
Penn.R.R
C I. 4 L
. . New Castle Pa
ia CREOCBNT PORT. CEM. Co ...
...Wampum, Pa
20- DiAMONDPoRT. CEM. Co........
21 SANOUSKY PORT. CEM. Co
2i ALMA CIMENT Co
23 LEHIOH PORT. CEM. Co
24. YORK PORT. CEM. Co
25. WABASH PORT. CEM. Co ...„
26- SANOUSKY PORT. CEM. Co.. _
27. UNIVERSAL PORT. CEM. Co , ., . .
... Middle Branch, Ohio
...Bar.RidjtTOuw....,
. . . Wcllston, Ohio
. ..WelUton.Ohio...
. . . Portsmouth, Ohio
. . . Stroh, Ind
... Syracuse, Ind
29. LOUISVILLE CEMENT Co...'.l^'.'. '. '.'.
30 KOSMOS POUT. CEM. Co
...Mitchell Ind
... Speeds, Ind
Kojmosdale Ky
B. 40. R. R....
B. 40. R. R...
L.4N
Sout'ernR. R...
Southern It. R...
A.G.S.R.R....
Southern R. R...
Southern H. R...
L.S. 4M. S
C.40
C40
Data, Ch
31. VmoiNiA PORT. CEM. Co
32. NORFOLK PORT. CEM. CORP .-
33. DIXIE PORT. CEM. Co
34. SOUTHERN STATES PORT CEM. Co.
35 STANDARD PORT. CEM. Co
. . . Fordwick. Va
. . . Norfolk.-Va
... Richard City, Tenn
. . . Roclimart, Ga
. . . Leeds, Ala. .
36 CASTALIA PORT. CEM. Co
3? SUPERIOR PORT. CEM. Co
38- IRONTOX PORT. CEM. Co ,,...
. . . Castalia, Ohio
. . . Superior, Ohio
• 'Includes all mills owned by company.
Fig- I95- Location of the Portland Cement
Plants of the Eastern Portion of the United
States in 1911. Below the Map Is a Tabula-
tion Giving the Name, Address, Capacity and
Shipping Railroad for Each Plant
A pin map like this can be quickly made up by using pins
such as are pictured in number 20 of Fig. 199 or pins such
as are used in Fig. 196. An outline map with the pins can
illustration like the above
pin has black figures on a
white background, and does
not give as striking an effect
as white figures on a black
ground.
Fig. 196 gives a hint of
what may be done to pre-
pare advertising copy with
almost no expense. The
illustration was made direct
from a map on which pins
were used having black
areas lettered in white. The
only hand drawing neces-
sary for this illustration
was about one minute's
work in darkening the high
lights where there were re-
flections from the surface
of the black pins. An illus-
tration of this type to show
the location of agencies,
branches, etc., makes effec-
tive advertising because the
black spots are so large in
comparison with the size of
the map that the whole
territory of the United
States appears to be well
covered by agencies.
Lettered or numbered
pins like those in Fig. 196
and in Fig. 199 are fre-
quently desirable to show
the daily whereabouts of
salesmen, repair men, etc.,
in order that the nearest man
may be telegraphed to in
be photographed directly to produce an
244
GRAPHIC METHODS
case of emergency. One prominent manufacturer of locks for bank
vaults uses a map which shows at all times the location of each of some
fifty bank-lock experts who are routed from city to city each day by
telegraph. The locations of the pins, and the railroad lines repre-
sented on the map, show instantly which man can best be sent to any
bank which reports trouble regarding the door of its safe-deposit vault.
Letters or numbers on the pins indicate the name of each man so that
there is no danger of an error such as might occur if the pins were
colored uniformly without specific letters or numbers.
Fig. 196. Map to Show the Location of the Selling Branches of a Large Manufacturing
Company
This line cut was made directly by photographing a standard map in which standard map pins had been
inserted. Black pins with white letters or numbers give excellent advertising copy with absolutely
no drafting work required
The argument of Fig. 197 would have been brought out better if
the railroad tracks had been drawn in heavy black lines across the city
map. Unless one is familiar with the city of Indianapolis, there would
be no way of explaining the heavy soot deposits in that section shown
on the lower portion of the map. Even the mention of railroad tracks
in the title does not make up for not showing them on the chart.
In preparing Fig. 198 a scale was very carefully selected to use one
dot to represent a definite number of people so as to avoid having dots
crowd each other too closely on the map. A map of this kind could be
made in a very large size, and then be reduced photographically to a
MAPS AND PINS
245
size which could be used in
a report or magazine article.
The reduction must ordi-
narily be so great for such a
map that considerable fore-
thought and care must be
used or the dots will not
show up distinctly enough
in the final illustration.
Anyone wishing to see many
maps of this type shown in
very excellent manner
should consult Volume II of
the Report of the Transit
Commissioner, of the City of
Philadelphia, published in
July, 1913.
In placing dots for out-
lying districts on maps made
by the method of Fig. 198,
judgment must be used to
have each dot placed at ex-
9 • • •
• •iff
•••
William D. McAbee in the Survey
Fig. 197. Relative Soot Deposits in Indianapolis,
March, 1912
The greatest soot fall is in the vicinity of railroad tracks
Carefully selected samples of snow were melted and the soot
of twenty-four hours weighed after the water was evapora-
rated. Spot maps of this kind can be quickly made by
using short map pins pushed in till the pin heads touch
the map
actly the right point to locate accurately the people represented. In Fig.
198 each dot represents two hundred people. A dot in the suburbs
may therefore represent all the people in one square mile of territory.
If a map were first made with two hundred dots for the two hundred
people, the one dot actually used on the final map would have to be
placed not at the geographical center of the area represented, but at
the center of gravity of the two hundred dots which it replaces.
In Fig. 199 various combinations are shown of pins, beads, etc.,
of use in map work. Data for map presentation are frequently so
complex that ingenuity is taxed to show the facts on any map of a
size commercially available. A great variety of effects may be se-
cured, however, by means of the devices shown in Fig. 199. The
exhibits given in the illustration are as follows:
1. Long pin with small size glass head, available in many colors.
2. Long pin of brass wire for use with beads as shown in No. 9.
3. Long pin with glass head used in conjunction with a piece
of sheet celluloid cut into the shape of a flag.
24G
GRAPHIC METHODS
PROPOSED ROUTES
*•
COMPREHENSIVE SYSTEM
PASSENGER SUBWAYS
FOB THE
CITY OF CHICAGO
ALSO
PQRJLATCN TAKEN FROM US CENSUS OF BO
tAOi DOT fiP^aC-vTS an PEOPLE
Tfte fntfneerfw Magazine
Fig. 198. Proposed Routes for a Comprehensive System of Passenger Subways for
the City of Chicago
On this map each dot is carefully located to represent 200 of the population. A spot map of this kind, made
to some scale whereby one dot represents several people, is essential to any reliable study of transit
facilities. After the spot map is made, the transit routes can be laid out to give the best service possible.
Short map pins with heads touching the paper can be used for dots on the original map
MAPS AND PINS
247
. I
6 7
8 9 10 11 12 13 14 15 16
22 23
Fig. 199. A Full-size Illustration Showing Some of the Different Arrangements of
Map Pins and of Beads Which Can be Used for Map Work
The size of the various beads and pins can be determined by measuring on the above picture with an ordi-
nary ruler, as the articles are shown in their exact size
4. A celluloid flag, with beads above the flag to represent quan-
tity, or beads in different colors to denote various characteristics
for the data portrayed. The grip of the sheet celluloid on the pin
is sufficient to hold both the beads and the flag at the upper part
of the pin.
5. Long pin with large size glass head, obtainable in different
colors.
6. Pin like that shown in No. 5 used with beads strung upon it.
7. A brass tack large enough to receive gummed labels which
may be written upon with a pen.
248 GRAPHIC METHODS
8. Map pins having sharp points and small spherical glass heads
in contact with the map. These pins are available in many dif-
ferent colors; the upper one in No. 8 is red and the lower one blue.
9. Beads in various colors of a size to correspond with the map
pins in No. 8. Here the beads were red. White beads, used for
every tenth position, show at a glance that there are 22 beads on
the pin. Note that the color red photographs as black.
10. Map pins having sharp needle points and spherical glass
heads in contact with the map. The pin is of the same general
style as No. 8 but it has a head of larger diameter. This pin is ob-
tainable in many colors.
11. Cloth-covered map tacks available in plain colors and in
plaids.
12. Single bead used with an ordinary pin as a crude substitute
for a regular map pin.
13. Beads in different colors corresponding in size with the map
pin of No. 10.
14. Beads of two different sizes representing different things
but at the same location.
15. Beads of two different sizes and three different colors. Since
both sizes and colors may be varied, and almost any number of
beads used on one pin, there are practically unlimited possibilities
for the showing of complex data.
16. Beads on a pin which holds down on the map a sheet of
colored celluloid cut to the exact shape of a small land area to which
attention is directed.
17. A sheet-celluloid marker held by a map pin like that seen
in No. 8.
18. Celluloid-covered tack, available in different colors.
19. Celluloid-covered tack with stripes of different colors.
20. Celluloid-covered tack with printed numbers from 1 to 99
inclusive.
21. Celluloid-covered tack having a rough surface so made that
the surface may be written upon with pencil or pen, yet erased
afterwards or rubbed off with a moist cloth. Lettering may be
made permanent by means of a coat of varnish.
22. Large size celluloid-covered tack available in different colors.
23. Large size celluloid-covered tack with stripes of different
colors.
MAPS AND PINS 249
24. Very large size celluloid-covered tack.
It will be seen from the foregoing list that the possibilities for
ingenuity in map and pin presentations are almost unlimited. The
celluloid-covered tacks having large flat heads, shown in Nos. 18 to 24
inclusive, are not as generally used as they might be for map work.
Map pins and tacks of this sort placed upon the surface of a map
can give a spot map with any desired diameter of spots, no matter
what size of map is used or what the amount of photographic reduc-
tion may be. It is simply a question of selecting from the spherical
heads, 8 or 10, and the flat heads 18, 22, and 24, to determine which
size head is best suited to the size of the original map and to the size
of dot desired in the finished illustration. Large celluloid-covered
tacks 18, 22, and 24 are also valuable to show the location of main
offices and different factories, or the locations of particularly im-
portant distributing points. The pins numbered 8, 10, 18, 22, or 24,
are five different sizes of pins which may be used simultaneously on
the same map to show different degrees of importance in the things
represented.
When used for photographing to produce an illustration such as
is shown in Fig. 196, lettered or numbered pins should have a black
background so that the black circle outlining the tack head will show
out in clear contrast against the map itself. This requires white
figures on a black or red background. Pins having red letters on a
black background cannot be used for photographing, as the red letters
would photograph black and disappear entirely, leaving a solid black
circle instead of a circle with figures. Since pins with a black back-
ground and white figures are not commonly obtainable, it may occa-
sionally be necessary to use pins like No. 20 in Fig. 199 having black
figures on a white background. Sometimes it may be feasible to
draw an ink-line circle around each number which appears in the photo-
graph so that the circles will be on the copy sent to the engraver who
makes the zinc plate.
When pins must be used to locate agencies, stores, or other things
which are usually concentrated in cities, the limitations are rigid
because all pins should be located on the map immediately above the
point representing the city. Crowded pins usually have to be spread
horizontally over a wide area, and when so spread out it is impossible
to tell which of several adjacent cities the various pins may represent.
Fig. 200 depicts what was done in one case to get over this difficulty,
250
GRAPHIC METHODS
, < ' • ./ t^*^>s v^B
"Modern Philanthropy", W. H. Atten, Dodd, Mead & Co.
Fig. 200. Sources of the First 3,000 Letters of Appeal Sent to Mrs. E. H. Harriman.
These 3,000 Letters Asked for $70,000,000
Eight different kinds of pins were used on this map to represent different kinds of appeals. Long pins like
those seen here are apt to fall out of the map, and thus destroy the accuracy of the record. Note the
area around New York shown on a larger scale at the right
as far as possible, by showing the more thickly crowded district as a
separate area on a larger scale placed at one side of the map.
The use of beads in conjunction with pins overcomes the main diffi-
culties encountered when pins alone are used. Beads may be placed
one above each other on long pins or wires so that each pin will be
exactly in the point on the map for each city, and thus portray nu-
merical data by map location more accurately than possible with other
methods. The adjoining cities can be clearly discerned by means of
separate columns of beads, whereas if pins alone are used the dif-
ferent groups of pins frequently blend so as to be indistinguishable.
If there is only one item to be represented in a town, single glass-head
pins may, of course, be used in conjunction with the beads.
When there are several units in a town, the beads strung on a
long pin or wire can be counted quickly if a bead of a different color
is used for every tenth bead, so the whole column may be counted by
tens as possible in Fig. 201. A bead map like Fig. 201 should be
mounted on several layers of corrugated straw-board to allow the
long pins sufficient depth in the mounting to hold fast. For this
MAPS AND PINS
251
particular map six layers of straw-board were used, giving a total
thickness of about 1J4 inches. Though this mounting made out of
corrugated straw board was thick, it was extremely light and very
convenient to handle.
J-JARVARD • -
- . UNIVERSITY
Fig. 201. Residence of the Men of the Class of 1907, Harvard University, Six Years
After Graduation. The Bead Wire for Boston Includes All Men Living within
Twenty-five Miles of the City Hall
Beads on long pins and wires were used here when there was more than one man in a town. A white bead
was used on the wire for every tenth man. Counting from the top by tens, the exact number in any
city can be seen from the illustration. 711 men are represented in this illustration less than 5 inches
wide, yet the number in each city can be counted accurately
If long columns of beads must be used as in Fig. 201 for New
York and Boston, the beads may be strung on piano wire such as
may be secured in any good hardware store. The piano wire should
be heated in a gas flame so as to remove some of the spring temper.
After the wire has been heated it can be straightened and it will re-
main straight without continually springing back into coil form.
252 GRAPHIC METHODS
Brass wire should be used if the holes in the beads are large enough
to take wire of a diameter sufficient to give the required amount
of stiffness. Brass wire is not as stiff as steel wire. When small beads
must be used having small holes, the combination of wire and beads
may be given several coats of varnish, if necessary, to make a tall
bead column stand up straight. The columns for Boston and New
York in Fig. 201 had to be varnished as the wire was very small on
account of the fact that the diameter of the beads was only about
-ft inch.
The bead map in Fig. 201 gives a great quantity of information
in a small amount of space. The illustration depicts the whole United
States on a page width of only 5j/g inches, yet all the facts represented
by the beads are brought out clearly. The men of the group por-
trayed who reside in foreign countries are indicated by pins near
the seacoast with arrows pointing toward the country of residence.
The fact that there were large numbers of the men in Massachusetts
made necessary an extremely long wire for the beads of the Boston
district. Because of the small size of the finished illustration and the
size of map available, large diameter beads could not be used, and the
bead wire for the Boston district was necessarily very tall and slender.
The Boston bead column was about as tall as could be used without
the column of beads bending under its own weight, even with the
bead column varnished.
Another difficulty in having very tall columns of beads is due
to the fact that the bead map must be photographed at an angle of
about 45 degrees in order to show a good picture of the map.
If the bead column projects more than a reasonable distance
from the map it is impossible to find a camera lens which will keep
in focus the whole map and the full length of the bead columns. Either
the map or the top of the bead column will be out of focus and there
is no way of overcoming the difficulty. When Fig. 201 was photo-
graphed the image on the ground glass of the camera showed at once
that the tops of the bead columns were out of focus. The bead wires
for New York and for Boston were accordingly pulled entirely out of
the map and the map was photographed without these two bead
wires. The two bead columns were drawn in by hand on the surface
of a photograph measuring 8 inches across the base of the map. WTith
a little care, using a fine-pointed pen, bead columns such as these can
be drawn in so that the ordinary observer would ^ever notice that
MAPS AND PINS 253
they were put on after the photograph itself had been taken. The
angle at which the tall bead columns should slant can be determined
by observing other bead columns in the same vicinity. In the case
of Fig. 201, the angle was obtained by observing the bead column
for Philadelphia. The reduction in size from the photograph on which
the hand drawing was done, to the half-tone (in this case, a final re-
duction of from 8 inches to 4% inches) was sufficient to eliminate
most of the imperfections due to hand work.
The use of beads opens up a whole new field for map presentation
of statistical data. The Board of Sanitary Control for the Cloak
and Suit and the Dress and Waist Industries of New York city made
up two bead maps showing the fire risks and the sanitary condition
in all the twenty -five hundred factories which come under the super-
vision of that Board. One bead on the map represents the condition
for each factory. On the fire map the height of the multi-story loft
buildings in which the different factories may be found is indicated
by using one bead for each floor. Thus, in some of the taller build-
ings, twenty stories are indicated. Different colors of beads according
to the fire risk or the sanitary defect to be shown mark the stories
very plainly, and the heights of the bead columns show the heights
of the buildings so that the bead map itself represents in miniature
the sky line so typical of Manhattan Island.
Bead maps carefully made up should be of great use in preparing
illustrations for advertising purposes. The accuracy of a bead map,
when data for different cities must be shown, is much greater than that
of a map on which only pins are used. The bead map makes possible
the giving of information in condensed form with that great clearness
and accuracy necessary to good advertising. It can safely be pre-
dicted that pictures of bead maps will in the future be a common
thing in the advertising pages of magazines.
CHAPTER XIII
CURVES FOR THE EXECUTIVE
i
WITH the exception of the railroads, there are relatively few
businesses which make a practice of plotting curves to show
operating records in convenient form for the use of executives.
Railroad accounting is more highly standardized than accounting in
industrial corporation work. The standardized method of accounting
has made it rather easy to compare the operating records of different
railroad divisions and of different railroad systems. It is probably for
this reason that railroads have adopted the use of curves for operating
records so much more extensively than have industrial or mercantile
businesses.
The upper curve in Fig. 202 is plotted according to the method used
on many railroad systems. In this form of plotting a month may be
said to be represented in the middle of a space between the vertical
lines. Horizontal lines are drawn in the space for each month to a scale
representing the figures which it is desired to chart. Lines are then
drawn vertically to coincide with the vertical lines of the co-ordinate
paper, and they join the horizontal lines of different months in such a
way as to give an effect like that of a stairway.
Curves for the same data plotted by the method shown at the bottom
of Fig. 202 are much easier to read than those plotted by the step method
shown in the upper portion of the illustration. By the method in the
lower part of the illustration the plotted line more closely approaches a
true curve, there is much less variation in the direction of the lines from
month to month, and the general trend of the curve line is easier for
the eye to grasp. Compare the two curves for the summer months of
the year 1909-10. In the upper curve a series of steps, and in the lower
curve an almost straight line from April to September inclusive, indi-
cate an increase by fairly equal increments during those months.
Certainly equal increments are more easily represented by the straight
254
CURVES FOR THE EXECUTIVE
255
200000
18OOOO
16OOOO
14OOOO
12OOOO
1OOOOO
8OOOO
6OOOO
4OOOO
2OOOO
O
2OOOOO
18OOOO
16OOOO
14OOOO
12OOOO
1OOOOO
8OOOO
6OOOO
4OOOO
2O COO
O
19O8-O9
1909-1O
191O-11
Fig. 202. Total Sales of the "Metropolis" Branch House of the "R.S.T." Automobile
Company for Three Years
These two curves are plotted from exactly the same figures. The upper curve is drawn by the method
still used by some railroads, but generally going out of use. The lower curve is plotted by a simpler
method which should be universally used
line as in the bottom curve than by the ragged series of steps shown
in the upper curve.
Another disadvantage of the method of steps with flat tops as
compared with the method using slanting lines and peak tops, is seen
when two or more curves are so drawn that they intersect on the same
sheet of co-ordinate paper. Curves plotted with peak tops can be
drawn very close together and yet be fairly distinct from each other, as
will be noticed in many of the illustrations in this book. If, however,
two curves with flat tops like those shown in the upper portion of Fig.
202 are plotted in such manner that they intersect each other, the re-
256
GRAPHIC METHODS
7+ot
JAN
FEB
MAR
APR
MAY
JUNE
JULY
AUG.
SEPT
OCT.
NOV.
DEC
TOTAL COST
3* 11
<t+ 37
<yfe is
O 0 O a
<?^ *7
77 29
7<f 5J
<?.? /.f
6« 77
JJ J*
VS-75
SO &>o
NO OF TONS
2ik
*J7
to<}
VJJ
Ji<f
"J2
J 70
V-9S
f-»6
jro
JSe
S~7*
COST PER TON
./S3
2t5
2J4>
./s*
.^5"f
./73
2/Z
/&£
/jy
o<?s~
/,
'^
OS8
_ 275
0 250
0) g 225
Q C 2OO
2 0 15°
0 |2 IOO
m <r °75
3 IiJ .050
a .025
^^^
/
\
9B
f~~
s
/
J
/
\
/
^
^
/
\
r
s
^
^
^^
V
s,
*-"
sxfc,
^
Courtesy of Factory
Fig. 203. Lubrication Cost per Ton of Product for a Factory in the Year 1908
The 6gures at the tqp of the co-ordinate ruling give the data from which the curve was plotted. Though
data should be put on alf charts, Bgures arranged in the direction here shown are not in convenient form
for addition. See the later illustrations in this chapter for methods of placing Bgures above each point
on a curve
suit is very confusing on account of the fact that the vertical lines con-
necting the flat tops may coincide. When one line falls directly on top
of the other, there is- no way for the reader to judge which curve is
which beyond the point of intersection. Unless the curves are very
carefully colored or dotted there is great danger that the reader will
jump from one curve to the other in his interpretation of curves which
happen to meet. This weak point in the flat-top method is particularly
noticeable if blue prints must be made from original charts in which the
flat-top method is used. On the original chart the curves can be fairly
well distinguished by using different colored inks, but as the colors are
lost in blue-printing, each blue print must be colored by hand, using
the original chart as a key to show what the colors should be. If a peak-
top method of plotting is used, numerous curves may be run across the
same sheet and yet be distinct enough for identification even when all
are reduced to uniform white lines on the blue print. It would be easy
to name fifteen reasons why the method of plotting with peak tops is
superior to the method of plotting with flat tops. The advantages of
the peak-top method seem so obvious that it is believed the reader
will agree to its desirability, without further argument being given here.
The man who plots a curve has before him the data showing the
actual value for each point plotted on the curve. If any questions
arise in his mind regarding the comparative figures at different points
on the curve, he can refer to the data from which the curve was plotted.
CURVES FOR THE EXECUTIVE
257
CD CZ.
ce
Q-
•<
CD 0- K
Z3 l_l O
<C </•> o
o
C£UW
2100
2000
1900
1800
1700
1600
1500
1400
1300
1200
1 \ OOj
j
IE\
^N
UEi
3
I
L
,
L
Y
N
v.
^
7
N
1000
900'
Anni
|
A
\
/
X
?
^>
/
\
S
t
:
3X1
>E>
SEf
i
,
/
^ — ^
_J
OULT
700'
600
500
400
30Q
7flfY
>----<
^
^
^
J
J
NE
TI
.EV
EN
UE
/
^ — <
/
N
/
r^
7
:
i
/I
^
\
^
100
c\
CALENDAR YEAR
The man who reads the curve, how-
ever, must ordinarily get the value
of any point on the curve by refer-
ring to the scale on the left-hand
margin of the chart. As most points
on curves do not fall exactly on the
horizontal co-ordinate lines, the only
way in which the actual value at
any point can be determined is by
careful estimate of the fractional
distance between horizontal lines,
according to the scale shown on the
margin. The resulting value for
the point is ordinarily more or less
inaccurate, depending upon the scale
to which the curve is drawn. Not
only is the reader's time taken in
estimating the value for any point
on the curve, but when he gets his
result he is dissatisfied, for he cannot
feel that the figure obtained is really
accurate. There is a great advan-
tage in showing on a chart the figures
from which the curve was plotted.
When only one curve is shown on a
chart it is very easy to give the
figures immediately above each point.
The method used to show the figures
in Fig. 203 is not, however, satis-
factory, as the figures do not fall
in a column. The method of indi-
cating figures shown in the illus-
trations later in this chapter is much
superior to the method of Fig. 203, and
should be adopted as general prac-
tice by anyone preparing curves for
record purposes, or for executive use.
1912 o
1913 •
Bureau of Railway Economics, Washington, D. C.
Fig. 204. Monthly Revenue, Expense,
and Net Revenue per Mile of Line
for Railroads in the United States
Having a Yearly Revenue of One
Million Dollars or More
This illustration shows one of the difficulties encountered when curves for successive years are plotted on
the same co-ordinate ruling. Here the data of January, 1913, are indicated by a dot rather than by a
line. The change occurring from December to January is not easily seen. This difficulty can be
easily overcome by allowing an extra space for one month as in the following illustrations
258 GRAPHIC METHODS
In Fig. 205 a curve is shown drawn upon a carefully designed four-by-
six-inch card form. This card is designed for the plotting of data for
one year by months. Thus, the fiscal year of a business can be shown
on one card. Succeeding years are entered on different cards, so that
by arranging the cards chronologically variations from year to year
may easily be seen. In order to avoid the difficulties pointed out for
Fig. 204, and Fig. 104, thirteen vertical lines are used on this four-by-
six-inch card. At the beginning of each card the last month of the
previous fiscal year is repeated. In Fig. 205 the fiscal year begins in
August. At the beginning of the card we repeat the line for July, so
that instead of showing a dot when the August figures are plotted we
are able to draw a line showing the change which has occurred from
July to August. In general, it is good practice to use one more vertical
line than there are points to be plotted, so that the last point on one
curve, sheet or card may be repeated on the next curve sheet or card.
Figures representing the value for each point on the curve are given
immediately above each point, in the case of Fig. 205 to the nearest
dollar. Figures for cents could, of course, be given if desired, but for
executive purposes it is usually better to neglect the cents in all large
numbers. The arrangement of the figures shown in Fig. 205 is such
that at the end of the year the figures can be added quickly and the
total given on the card. Cards for different years can easily be looked
over and the yearly total figures compared instantly, to the great ad-
vantage of the executive who has these additions made for him and
recorded where they are always in plain sight. Curves as they were
used in the past gave the values of single points only, without any
summation for a series of points. In Fig. 205 we have not only the
yearly total, but also totals for every three months, so that the total
for any quarter of the fiscal year can be compared with the total for
any other quarter.
Fig. 206 represents a four-by-twelve-inch card used to plot data for
fifty -two weeks in one fiscal year, the last point of the preceding year
being repeated at the left-hand margin. Figures for the repeated week
are not given above the co-ordinate ruling, as the repeated figures might
then be included in the additions and cause serious error. By repeating
the point, however, and not repeating the figures, the curve is made
continuous without any danger of adding too many items into the total.
In the right-hand margin of Fig. 206 a short vertical line may be
seen. This line may be used as the shank of an arrow to indicate, as
259
H— -b
r
P "p
1
11
—
1
' w .Ss
1 5 &8
§ gt; .
« s ^^
j.
9SQ O£ 1
/
/
m
S *^ 2
Jtl.>JI
d
/
T
in
"^ OUD'O
Si ^ «-
03 Uf5
V j S'C
I
Nfil|
/
^.
d uJ-c i
Js
jj
f
(0
/-\ P i,-0
? S«g
»5 '33 c t=
\
s
flfl
S ^ u^
2 t
V
tf i. U5
3 re u c
« -"28
\
\
(M
<« o «sg
f^s§
N
1
111
o ~zi *T
S 41*3,0
** •""T'l
/
A 5Sl
(_l ft "* «M
^* GOft't £
/
O
o^o
/
A
C
**^ «« "S
0 «o|?
3-^.2^5
7
\
<0
3 S^^
•3 d c
^ rl#e
i
CO .5 o 5
T3 50^
H «,, u ft
1 <
8 c
) C
> c
> C
1 £
:s
> c
c
c
f C
> <
['
1 (
c
c
\ c
> c
I C
• <
>i
II
j-j
• -
lc
1
S H^
• **53
8 -a B s
.3 u a; r*
i i
«
vo <r
ol •"
lftB*Wfi*
>'c
> c
)«
0
• fl
c
*•
«
c
i!
o
c
u
•
'/<:
1 C
k r
^/
!S
J F
\\
on
) C
) P
>
)
1
^ a^ *
O^ J^-a;
^ g §5
rt -Si °
a *%°
.a ||«
•* ^ fe'C
<fi «>^ <?•
^ "H.SPi
10 51s
•*• OJ f— I
O (ft — ' C
r-r. o "> •*-•
• ^ dj c
l/ .S
E§S.
<
360
CURVES FOR THE EXECUTIVE 261
in Fig. 205, in which direction the executive desires that the curve should
trend. In Fig. 205, which represents total sales, the head of the arrow
of course points upward. If the curve is to show expenses per
unit of output, the head must be placed on the vertical line so that the
arrow will point downward. In Fig. 206 no head is placed on the arrow,
as fluctuations in a payroll mean nothing unless we know the output of
work. An increasing payroll may result either from increasing sales
or from inefficient production. A decrease in payroll may result
from increased efficiency of production or because sales have fallen
off undesirably. Accordingly, no head is placed on the arrow and the
curve must be interpreted by conditions other than those shown on the
face of the card itself. In general, all curves relating to total money
expenditures may trend either up or down, without meaning anything
unless other conditions are considered. It is only when we express
expenditures as expenditure per unit that we really get a curve for
which it is safe to say that we should always desire a downward trend
as long as quality is maintained.
Forms for executive records such as are shown in Fig. 205 and Fig.
206 should be printed on an especially high grade of paper. Most paper
in use to-day contains sulphite pulp and chemicals which cause more or
less rapid deterioration. The paper commonly used turns brown and gets
brittle within five or ten years, so that records on this paper are likely
to become useless in a comparatively short time. High-grade paper to
be used for the record cards shown in Fig. 205 and Fig. 206 should con-
tain only the finest selected linen stock and should be guaranteed ab-
solutely against any deterioration for twenty years. The chief advan-
tage of such paper, however, is that it can be used in card form, yet
be transparent enough to allow of blue-printing.
The time required to blue-print cards made from such paper may best
be compared with the time necessary when ordinary tracing cloth is used.
Blue prints are also frequently made from bond paper. Bond paper re-
quires an exposure of, roughly, three times as long as tracing cloth.
A special card made of heavy paper would require an exposure of about
six times as long as tracing cloth, or twice as long as bond paper.
When sunlight is used for blue-printing, there is no difficulty
in getting a sufficiently long exposure to make good blue prints from
the card forms shown in Fig. 205 and Fig. 206, if the forms are printed
on selected paper. Should electric blue-print machines be used, however,
it may be found that certain of the older types of continuous printing
262 GRAPHIC METHODS
machines cannot be run slowly enough to give the required length of
exposure. Some of the older machines can be changed at rather slight
expense so as to have an extra belt-pulley reduction between the motor
and the blue-printing machine itself. The newer types of machine
can usually be run slowly enough to give the exposure necessary for
this heavy paper. If a new blue-printing machine is to be ordered,
however, it is well to make some preliminary tests with the cards.
The cost is not great for blue-printing a whole set of record cards
once each month after the last data have been plotted. Blue-print
paper of heavy weight should be carried on hand, already sensitized
and cut to size, four by six inches and four by twelve inches. The
original curve cards, each backed by a sensitized card of the same size,
are simply fed into the blue-print machine as rapidly as the operator can
put the two cards together in pairs.
There is a tremendous advantage in having all curve records made
on a high-grade transparent card so that any card may be duplicated
by blue-printing whenever desired. It is impossible for anyone to
predict what conditions will come up in the future of a business, and
the only safe plan is to install from the start such a curve-record system
that any card may be duplicated by blue-printing in future years if
desired. It frequently happens that an executive wishes to have a blue
print made of a recent year's curve card to compare with the curve
card of an earlier year, in order that the blue prints may be mailed to
some higher official or to some branch-house manager to point out certain
conditions which it would be difficult to describe fully if copies of the
curve cards could not be sent. Unless, however, the curves for the
earlier years are made on cardboard from which blue prints can be
taken, it is impossible afterward to make duplicates of these cards
except by hand copying or photographing. In many cases it will be found
desirable to take a blue print of every record card once each month, so
that blue prints may be sent each department head to show him the
exact condition of his department as a guide for the next month.
The space toward the left-hand side of the cards shown in Fig. 205
is for remarks which may be necessary to explain different fluctuations
in the curves. In Fig. 206 full circles along the curve show those weeks
in which a full holiday reduces the amount of the payroll. In the month
of April there was, for this particular plant, a half -holiday on the nine-
teenth. This is shown by a half circle. At the end of the fiscal year we
see in Fig. 206 stars to explain why the curve showed a drop to less than
CURVES FOR THE EXECUTIVE 263
one-half in the normal size of the payroll. The plant was shut down at
the end of the fiscal year in order that an inventory might be taken.
The notes at the left-hand side of the card are absolutely essential to
explain unusual conditions affecting the curves. In two years after an
event, most managers are entirely unable to explain certain peaks or
valleys in a curve, though these extreme fluctuations may be due to
such events as fires, floods, or strikes. Unless the causes of unusual
fluctuations are recorded, the curves would have far less than their
possible utility to any new man who must take up the manager's task
as his assistant or as his successor. An example of the kind of informa-
tion which should be noted on the curve-card margin came up in a large
public-service company, where the manager was for several minutes
unable to explain a very great fluctuation which had affected the earn-
ings of a trolley company some two years before. After careful study
to explain the drop in the curve, he finally recalled that this trolley
line was in a city where all cars must pass over a drawbridge between
two sections of the town. At the time in question a steamer had col-
lided with the drawbridge, making it impossible for about two weeks
for any street car to cross. This accident caused the earnings of the
trolley line to drop greatly during the whole of the two-weeks period.
The cause of the unusual condition for the curve should have been
recorded for future reference.
In Fig. 207 we have the curves for three succeeding years placed one
above the other, so the eye can glance up and down the vertical lines
for months and see instantly the changes which have occurred during
the entire period. As automobile sales are very greatly affected by
the weather conditions of different seasons of the year, these curves are
important. Though weather conditions have affected the curves quite
largely, we can see, by comparing the curves for 1910 and 1911, that
probably conditions of management as well as weather conditions
caused smaller shipments in November and December, 1911, than in
those same months of 1910, when shipments were quite good. The card
for 1912 is shown with the curve incomplete, just as the manager might
have seen it early in the month -of February, 1912, after the January
reports had been received, tabulated and plotted. As Fig. 207 shows
curves which are true records of the real happenings in an automobile
plant, they are worthy of study for practice in curve interpretation.
Notice that the changes from July to August, in 1911 and 1912, are
readily seen because each curve card begins by repeating the record
GRAPHIC METHODS
2678
1910
So.tes — Tbtxxl
XV Z
Automobile Ttont-
f\ <p
V*
3oo,ooo
"2 "7 0,000
a -^0,000
•2. 10,000
I & 0,000
I 6 0,000
12.0,000
90,000
60,000
30,000
« n L'
(0 0»
Ol - W 10
w
CD
(D CD ~
ov CD n
ID C 0
270,000
^ 'Z-io.ooo
•^ a 10,000
0 180,000
190,000
-§- »:zo, ooo
•g 90,000
£>o,ooo
•30,000
"" O -
-7
•*^
*- .
s
s
'
"
Vx
^««
^
••*«*
w.
x
x^
V
S
•^^•v
s
*
9 tO II IZ I
34667
^ %1 0,000
(^ ^4o,00o
-S1 -2.io.ooo
S 1 Go, ooo
1 S0,000
^ 1 00,000
•g 90.000
€)0,000
3o,oo0
^ 0 -
s
^
^
/
**•
7 8 9 !O II \Z t
Fig. 207. Sales of the "X.Y.Z." Automobile Plant for Three Consecutive Years
The three 4-by-6-inch cards are arranged one above the other so that the curves for different years may be
easily compared. Note that November and December were good months in 1910, but poor months in
1911 and 1912. The 1911 card above is the same as in Fig. 205, but here it is printed in one color
only. Observe at the right the arrows showing that it is desired that the trend of the curve should be
upward. Arrows like this save about two-thirds of the executive's time in looking over a large number
of curves
CURVES FOR THE EXECUTIVE
265
for the last month of the
preceding fiscal year in-
stead of using a dot as
shown in Fig. 204.
The separate cards for
different years, which in
Fig. 207 are arranged ver-
tically one above the other,
may be laid horizontally as
in Fig. 208. Here the cards
are superposed on a black
background, the left-hand
and middle cards each over-
lying the card to the right,
so that the curve appears
continuous. The vertical
arrangement allows of a
very accurate analysis of
changes which have oc-
o
curred from month to
month of each year. With
the horizontal arrangement
it is not so easy to compare
any month of one year with
the corresponding month of
another year, but it is easier
to see the changes which
have occurred in a curve as
a whole throughout a period
of years. Thus in Fig. 208
it is much easier than in
Fig. 207 to see that sales
dropped seriously in the
first half of 1911, and that
they increased far beyond
any previous record during
the last half of 1911. The
vertical arrangement is use-
f ul for one purpose : the hori-
266 GRAPHIC METHODS
zontal arrangement is useful for another purpose. By having loose
cards, we can arrange the cards either horizontally or vertically and
get all the advantages of either position. Curves plotted in loose-leaf
books, or on large sheets of paper, cannot have this flexibility of arrange-
ment, and they accordingly handicap the executive in the analysis
of data which may be vital to the success of his business.
When the cards are arranged horizontally the figures for the curve
over a series of years are in plain sight, while in the vertical arrange-
ment one card hides the figures on another card. Figures are essen-
tial to the true interpretation of curves like those seen in Fig. 208.
In looking at Fig. 208 most readers are likely to feel that the business
of the year 1911 was much better than the business of the year 1910.
When we look at the total figures, however, we see that the sales
for the year 1911 were only $1,435,041, while the sales for 1910 were
$1,575,298. Not only were the total sales for 1911 much less than the
sales for 1910, but there was a very great fluctuation in sales from
month to month which created a very difficult problem in the opera-
tion of the manufacturing plant. In the early half of the fiscal year
ending in 1911, men were not needed because of the small volume
of sales, and a large portion of the working force had to be discharged.
In the latter half of the fiscal year, sales increased so rapidly that men
had to be hired in large numbers. Inevitably, therefore, many un-
skilled men were obtained who were sure to spoil a large volume of
any output requiring the great accuracy needed by automobile parts.
The record for the fiscal year ending 1911 was in every way bad, as
compared with that for the fiscal year 1910. The company eventually
ended in a receivership.
Cards only four inches by six are of sufficient height to hold the
co-ordinate ruling needed for curve plotting, and yet have room above
the ruled field for two separate columns of figures of seven digits
each, as well as space across the top for a title which may run the whole
length of the card. In Fig. 208 we have two sets of figures, one set
for months and the other set for quarters. Each set of figures con-
tains six numerals. Although the illustration in Fig. 208 is only
about one half the natural size of the card, the figures themselves are
clearly legible and the title at the top of the card is easily read.
One of the chief advantages in the use of loose cards lies in the
fact that any set of cards may be laid out on a table and compared
with any other set of cards in the manner shown in Fig. 209. It is
CURVES FOR THE EXECUTIVE 267
difficult with a loose-leaf book to arrange a system for keeping hun-
dreds of curves in such a way that quick comparisons between any
of them can be made. When loose cards are used any card can be
compared with any other card instantly, and, if desired, cards for any
curve for a series of years may be laid out for comparison with cards
for any other curve for any series of years. Anyone without experi-
ence in the analysis of curve records for large corporations may take
it as a fact that no system of curve records should be installed which
does not permit the instantaneous comparison of any curve with any
other curve in the whole system.
Fig. 207 and Fig. 208 show the shipments from an automobile
manufacturing plant as sales. Many of the automobiles recorded
as sold were shipped to branch houses owned by the same company,
to be stored there during the winter months when the branch-house
sales are very small, for the reason that people do not wish to buy
touring cars in winter. In Fig. 209 and 210 more curve records from
an automobile business are given. In these cuts also, as in Fig. 207 and
208, cards are shown in groups of three, photographed against a black
background. In Fig. 209 we have in the upper curve the actual
sales of an automobile branch house selling direct to the auto-
mobile user. Notice that the sales in the spring months greatly ex-
ceed the sales at any other time of the year. In the first two fiscal
years sales were at a maximum in May, while in the third fiscal year
sales reached the maximum in April and were fairly large in both
March and May.
In the lower curve we have the expenses of this same branch
house. A very noticeable increase in the expenses occurred in the
fall months at the beginning of the fiscal year, once in October and
twice in September. This increase was due to local advertising an-
nouncing the new-model automobile for the next season. It was
customary for all manufacturers of automobiles to announce their
next season's models in the fall months, and the peaks in the expense
curve shown here came as they did simply because of this custom
of the trade.
It is quite easily seen from the upper curves that the sales for the
second fiscal year were much greater than those for the first fiscal
year. The total figures, however, show much more clearly the extent
of the increase. Because of the excellent sales during the spring months,
the curve for the third fiscal year at the right gives the impres-
268
GRAPHIC METHODS
0^9'ass -^
oee-t^t- -^
T"nrr *
L ^
r
k - •>
v
i
V
r> I
\ •
, o
4 «
I L
9l8Xi,tt —
09S'SZ.
/ :
> u,
^
\ !
i
\
V M
:
-to
i
ct<.'iae
i
- ^ «
> K>
\
V «
\
^
t M
"
£~
^ o o o o o o
006000
o o o o oo
6 o" d o oo
{•iff
8°§§8
IJIJ«
§•«•
o 'eee-c
jj oze-b.
(0 tso-fc.
2 SAa-e
-,
r
\
z
S
I
eet»'t
5 9feE-e.
ie^ z
« r:
1 t"t-<8
9<»i/e.
1
\
L
>
/
\
966 "BE
6t»6-^
P B99'S
*
i
6trz-e
*-z*-a
9et'r
zis-z
3 'er«
„ ne-z.
S90-S
j *
/
'
y
/
s
s
OOB Bf- _
0 698 &
ice-z
!
5 «IIC>
f° ese-z
? ^Ctr-5
CiZ.'*
oi ^.ie-1
0 6Ct»Z
^ loi-s
j» 6 re's
IL96'l
»
<
6 S
P5
» ! t
? I S
10 U £
/
I
1
I
\
1
i
ll
i
X
x"
V,
^x
?oo 9090009
,88 §8888880
» o5 lr < • T P * J
*•««
^•Bs§
s ^ s
1^1
w
CURVES FOR THE EXECUTIVE
269
sion of a prosperous year.
Reference to the figures for
the total yearly sales, how-
ever, shows that the sales
for the third year increased
only very slightly over the
preceding year. When we
compare the sales of this
branch house with the ex-
penses, we get quite a dif-
ferent story from that read
from sales curves alone.
The increase in sales from
the first year to the second
year was very great and
without a correspondingly
great increase of expenses.
Putting the figures for the
first and second years into a
ratio, sales increased 64 per
cent, while expenses in-
creased only 10 per cent.
In the third year, however,
the sales hardly increased
at all, while the shape of
the curve for expenses
shows an almost constant
increase. A little * mental
arithmetic will show further
that with almost stationary
sales the expenses were per-
mitted to increase about
one-seventh or, roughly, 14
per cent.
Notice that in Fig. 209
arrow-heads mark a desire
that sales should go up. No
arrow was used in connection
with the curve for expenses.
270 GRAPHIC METHODS
It was permissible that expenses should go up in the second fiscal
year, for the volume of sales increased very rapidly. The cost per
unit of sales or the ratio of expenses to total sales had decreased greatly.
An arrow pointing downward would have given a wrong impression
as the total expenses had increased justifiably. It is better, therefore,
to avoid using arrows than to use arrows which would mean nothing.
The real story of this automobile branch house is seen in Fig. 210
which gives the profit-and-loss curve corresponding to the sales and
expense curves of Fig. 209. Expenses of the branch house were fairly
large throughout the whole year, because of fixed charges, while the
great fluctuation in sales caused a loss during the many months in
which the volume of sales was small. Note how much better the
profits were in the second year than in the first year, because the
business had been established long enough to have a fairly good vol-
ume of sales during the fall months. There was a profit in all the
months of the second year except two, with a total profit of very
considerable size, though not a tremendous one compared with the
volume of sales, since the profit was only 5.9 per cent of the sales.
In the third year the profits were on the ragged edge throughout
the whole year except in the three spring months of March, April,
and May when sales were exceptionally large. The total profits for
the year, even with a slightly increased volume of sales, were less than
one-third of what they had been for the preceding year.
Just to show what complex conditions enter into the comparison
of business curves of this sort, it is mentioned here that the small
volume of sales, the large expenses, and the negligible profits in the
first half of the third fiscal year were not the fault of the manager of
this branch house. The trouble went back to the factory engineering
department which failed to get its next season's models designed early
enough. Consequently the car could not be manufactured in suf-
ficient quantities to give the branch manager enough cars to make
a satisfactory volume of sales. The branch manager blamed the factory
because the factory could not deliver a sufficient quantity of cars. The
factory manager was not to blame, however, as the engineering depart-
ment (reporting direct to the president instead of to the factory man-
ager) had delayed the design for the new car, and the factory manager
was, of course, unable to build a car until he had the drawings. This
example will perhaps give a fair idea of the uses which can be made of
curves plotted from the operating figures of a complex business.
CURVES FOR THE EXECUTIVE 271
A person who has not tried plotting curves on cards only four inches
high is likely to say that the card is not of sufficient height to permit
satisfactory curve plotting when there is a great fluctuation in the curve.
Such a person would argue that the card is not high enough to allow
the plotting of curves on a scale sufficiently large for easy reading, and
that any curve for a constantly increasing business is likely to run off
the top of the co-ordinate ruling within a few years. The curves as
shown in this chapter certainly vary enough to allow the eye to see all
the changes clearly. As the curves are in each case accompanied by
the actual figures for the value of each point on the curves, it is not
necessary that one should be able to measure accurately for points
falling between horizontal co-ordinate lines. Instead of consulting the
vertical scale to get the value at any point, reference is made to the
actual figures above the various points. These figures indicate a finer
fluctuation in the curve than it is possible for the eye to appreciate
even in curves plotted on very large sheets of paper. Figures, then, in
conjunction with curves like those shown here, make it unnecessary to
plot lines of such fine width or great accuracy as would be necessary
if the figures were not shown above the curve.
In Fig. 207 the bottom card shows the zero line extended to the left
over the figure seven at the lower left-hand corner of the ruled field.
On the middle card the zero line has been extended to the right. This
right-and-left extension of the zero line is not made until a card has
been completely filled out. The extension of the zero line indicates
the point at which cards are to be joined when laid in the horizontal
position shown in Fig. 208. It will be noticed, in Fig. 208, that the
cards are overlapped in such a way that the right-hand edge of the
uppermost card coincides with the left-hand edge of the ruled field
of the lower card, and that the zero line is continuous. The extension
line drawn at the left of any lower card shows where the extension
drawn across the right margin of the upper card is to be joined. Cards
may be laid together in a horizontal position almost instantly, and cor-
rectly, when these joint lines are present as a guide.
If, as in Fig. 211, a curve should rise with such rapidity as to be
dangerously near the upper limit of the ruled portion of the card, the
joint lines may be so drawn as to allow more vertical space on the suc-
ceeding cards. In Fig. 211 the curve for 1910 indicated that the curve
for 1911 might go higher than the 1,400 line. Consequently, when
the new card was made out for the year 1911, the joint lines were so
GRAPHIC METHODS
drawn that the line
at the right of the
1910 card was above
zero, and the joint
line at the left of the
1911 card at the bot-
tom of the ruled
field. Thus, when
the two cards are
overlapped so that
the joint lines match,
it is seen that there
is enough space in
the ruled field at the
right for the curve to
rise to the scale line
for 1,600. Two more
spaces were again
allowed in 1912 in
anticipation of even
further upward pro-
gress in the curve.
As joint lines may be
drawn in continua-
tion of any horizontal
line on either the
upper or the lower
card, any amount of
expansion in future
years may be pro-
vided for. The curve
cards are small
enough to be very
convenient to handle
and yet they may
be joined together in
such a way as to
provide for unlimited
future growth.
CURVES FOR THE EXECUTIVE 273
The card for 1910 in Fig. 211 has a broad line drawn by hand to
show the zero line. On the card for 1911 the scale begins at 400, and,
because the scale does not begin at zero, the bottom of the co-ordinate
field is marked with a wavy line. This wavy line is made very rapidly
with a pen and serves the very useful purpose of safeguarding the
reader from interpreting the curve as if the lower line on the field were
zero. Whenever zero is not shown at the bottom of the ruled field,
this wavy line should be used. Any card can thus be read independent-
ly, with safety so far as its interpretation from the zero point is con-
cerned. When several cards are laid out together, and the zero line is
shown on the left-hand card, as in Fig. 211, it is a simple matter for
the eye to imagine the zero line extended to the right below the other
cards, thus permitting easy interpretation of all cards.
It sometimes happens, especially in plotting costs, that the desired
direction of the curve will be downward instead of upward. In such a
case, and to show small fluctuations from month to month, the scale on
the curve cards may be so selected that the zero line does not appear
even on the first card plotted. Should the costs be reduced so rapidly
that the curve tends to run off the bottom of any card, the card for the
succeeding year may have the joint line drawn in such a way as to
allow an extension of the scale downward, exactly as Fig. 211 shows an
extension of the scale upward. By drawing the left-hand joint line
on the later cards above the bottom of the ruled space, and by putting
the right-hand joint lines for the first cards at the bottom of the ruled
curve field, the series of curves can be made to progress downward to
any desired extent in exactly the same manner as the curves in Fig. 211
progress upward year by year. By the use of these joint lines a
thoroughly universal arrangement of cards may be secured, allowing
extra space for movement either up or down.
Joint lines were devised chiefly to permit of showing a large up-
ward or downward progress in the curves for succeeding years with-
out the necessity of laboriously replotting the curves for the earlier
years. The desired result has been very satisfactorily attained. Should
anyone, however, object to the presenting of a series of cards in steps
as in Fig. 211, he need only replot the curve for the earlier years to
some smaller scale. In general, however, it will be found that prac-
tically no replotting is necessary or desirable. By connecting the cards
with joint lines and by using a wavy base line when the scale does not
extend to zero, all necessary convenience and accuracy may be secured.
274 GRAPHIC METHODS
When plotting curves on large sheets of co-ordinate paper it fre-
quently happens that the scale desired cannot be placed upon the
kind of ruled paper available. Scales must usually be made in full
size, one-half size, one-quarter size, etc., and it is usually too big a
jump to change from one of these sizes to another. The ideal arrange-
ment is to have a supply of co-ordinate paper with different rulings
so that when one ruling does not suit, some other ruling may be used.
On the curve cards shown in this chapter the horizontal scale is fixed,
as the cards are designed for use with definite units of time, such as
one year by months, one year by weeks, five years by months, etc.
For the vertical scale, however, two different rulings are provided.
One of these rulings has seven i-inch spaces as may be seen in Fig.
211. The other ruling has ten vertical spaces of i inch each as seen
in Fig. 209. The ratio of the two scales is seven to ten or, roughly,
one scale may be said to be two-thirds of the other. This is the most
desirable arrangement that it is possible to get, as these two rulings
afford a great range of scales to choose from. If by using one ruling
the curve comes too high on the card, simply change over to the other
ruling and the peak will come lower down on the card. The two
rulings, either in full size or in some fractional size, give every pos-
sible combination of scale that need be desired.
The ruling having vertical spaces of one-sixth of an inch is ten
spaces high. This ruling is very convenient for curve plotting on a
percentage basis when 100 per cent is shown at the top of the chart
as in Fig. 126, Fig. 128 and Fig. 129 in Chapter IX. If, on the ten-
space card, each Space is used to represent 10 per cent with zero for
the bottom line and 100 per cent for the top line of the chart, the
neatest possible arrangement is secured.
In starting to plot a curve which is to be continued year after
year, it is ordinarily best to allow plenty of room for future growth.
In the upper curve 'of Fig. 209 the scale was purposely selected for
the first year so that the curve would extend only about one-third
of the way to the top of the ruled portion of the card. This would
allow the sales to be trebled in volume before the curve would extend
over the top of the ruled portion and necessitate a change in scale
or a step upward so that the zero line could no longer be shown at
the bottom of the card. It is well to start all curves for output or
sales at about one-third of the height of the card so as to allow plenty
of room for future expansion. Curves for expenses per unit, however,
CURVES FOR THE EXECUTIVE 275
may be started well up on the card if there is any hope whatever of
reducing the unit expenses in future years.
The man who plots curves on the cards described here keeps a
supply of the printed cards in each of the two rulings of seven spaces,
high and ten spaces high. When starting any new curves he uses
whichever of the two cards gives the scale best suited to his purpose.
The cost of carrying two different kinds of ruled cards on hand is
negligible compared with the great convenience resulting.
The ruling of the cards in which the vertical spaces are either
1-inch or ^-inch high permits the use of an engineer's scale in forti-
eths or sixtieths of an inch, if it should ever be desired to locate plot-
ted points on the cards with very great accuracy. The engineers' scale
in fortieths or sixtieths of an inch gives ten divisions to each space
between the horizontal lines on the card and makes it possible to locate
each plotted point with a very finely sharpened lead pencil or a needle.
Practice, however, proves that there is no necessity for using an en-
gineer's scale in plotting curve points on the cards here described.
The man doing the plotting learns very quickly to locate the points
by using only the eye and a hard lead-pencil, so that the points are
practically as accurate as if spaced with an engineer's scale and a
needle point. Even if the points on the curve are not located quite
so accurately as they may be when a needle point and a scale are
used, it makes no difference to the executive by whom the curve is
read. The figures denoting the value of each plotted point are given
immediately over the point in the upper margin. The executive
reading the curve does not have to refer to the vertical scale. He
need only glance at the figures above any point to learn the value
for that point far more correctly than would ever be possible with
even the most accurately plotted curve if the value of the point had
to be interpolated from the vertical scale of the chart. The vertical
scale of these cards on which the figures are given in the upper margin
fulfills almost no purpose except that of giving a record of the scale
to the man who must plot points in succeeding months, or that of
giving the values of horizontal lines which are convenient in locating
high points or low points on any curve.
When another point has to be added on a large number of curves for
a succeeding month or week, the most convenient procedure consists
in first copying upon all curve cards, immediately above the vertical
line for the proper month, the figures from the typewritten reports, or
276
GRAPHIC METHODS
I iZ-'fil
f
s*
/
L
\
\
/
/
'
]
1
\
1
\
fece 01
f
y
f
\
\
N
•*V <
V
>
!{
!!
1!
; «
•» «
\ c
•s
i
i
f 8
3 n
o o
0 0
o IA 0
5
. i.
> (
X U
1 s
^
>
3 pi
1 01
« t-
other sources of informa-
tion. This is straight
clerical work and may be
done with a pen on one
card after another with
great rapidity. Ordi-
nary liquid drawing ink is
the best for the figures, as
the opaqueness of the
drawing ink gives better
blue prints than are ob-
tainable from writing ink.
This is often partly trans-
parent and prints pale
blue instead of clear
white. After the figures
have been entered on all
the cards, the cards are
taken rapidly one by
one and a sharp lead-
pencil is used to mark
on the proper vertical
line a point which, ac-
cording to the vertical
scale, corresponds with
the newly recorded fig-
ures in the upper margin.
When all the curve points
hav« been located by
lead-pencil marks on the
curve cards, a drawing
pen is used to draw the
line on each card to show
the change that has oc-
curred since the previous
point was plotted. As the
new point has already
been indicated in each
case by the lead-pencil
CURVES FOR THE EXECUTIVE 277
mark, all the ink lines can be drawn in rapidly with a draftsman's
ruling pen. If the suggested procedure is used, the lines may be drawn
so rapidly that there is no chance for the ink to dry on the pen and the
ruling operation is almost continuous.
In Fig. 212 we find on a reduced scale the same card that was pre-
sented in Fig. 206. Fig. 206 was drawn to full scale in order to show
the true size of the figures and the actual spacing. Fig. 212 gives a
better idea of the proportion of this card, and though of reduced size,
it nevertheless shows the appearance of a card suitable for the plotting
of records for one year by weeks, and thus requiring fifty-two entries
of figures in the upper part of the card.
In Fig. 212 the arrangement to show the dates along the bottom of
the card, with short vertical lines dividing the horizontal scale into
months, is not put on to the card until the exact year is known for which
the particular card is to be used. Lines dividing the year into months
so as to show exactly how many weeks are included in each month and
at just which portion of the week the beginning or end of each month
may occur are then put in by hand. In Fig. 212 the card has been used
for a fiscal year beginning August 1. The card is marked 1911,
meaning the fiscal year ending July 31, 1911. By referring to the
calendar for the year 1911 one may see how the short lines for months
are put in. As the pay weeks ended on Thursday, there were only four
pay weeks ending in July, but there were five pay weeks ending in
March. March 1 came on Wednesday. The last day of March was on
Friday. The vertical co-ordinate lines for March show clearly that
there were five Thursdays, and they also show the exact time relation
of the Thursdays to the beginning and to the end of the month.
After the month scale for any fiscal year has been marked by hand
on one card, any office boy can quickly copy the scale to other cards by
superimposing the first card on the next card and copying the pen
strokes from the first onto the second card. A supply of cards for any
year can thus be made up at small expense, without having to have
cards printed differently each year just because mankind has not yet
made a calendar which always has the same relation between days of
the week and days of the month. The scheme of indicating the rela-
tion of weeks and months by the short vertical pen marks permits the
carrying on hand of a supply of printed cards which can be used for
absolutely any fiscal year without danger of having to send the supply
of cards to the scrap basket, as calendars are sent to the scrap basket
278
GRAPHIC METHODS
"•
Si
o.
*
OQ'SZZ
LB- 1 G.Z
• £9 'bee
Zf6SZ
3TL93
*»•••»
E
»
1
(f)
oh-s ie-
^0.9 st-
Ofi'irbZ
90'9Be
oo-t sz-eta
0^-9 os-a i c
88-J^EC
E9'SSC
CL-SSC
oe-s <>9-9t,C
I8'9C£
SZ-XSE
OQOOOOOOOO
fl CJ
•> ^
11
CO o
£-3
p<
> p,
O .2-0
o g a
a ;S
o ^
1
13
o
.a 5
53 _l>
M &S
bfi
« s
I— ^1 --
— -
^ _.
.3-3 *
just because last year's
calendar is of no use
after December 31.
This assurance of a
perennial form instead
of one which must be
renewed or replaced
every year is no small
advantage. Figures
designating the months
for any fiscal year can
be printed on the week-
ly card if desired. In
Fig. 212 the figures 8, 9,
10, etc., indicating the
months, can be printed
on the cards and thus
leave to be inserted by
hand each year only the
short vertical markings
indicating the relation
of the weeks and the
months.
Fig. 213 shows the
weekly curve card
used in the records
of a dairy farm. The
particular curve shown
is for a prize Jersey
cow which was being
very carefully tested
in the hope of break-
ing the world's record
for milk production.
The milk production
each week is indi-
cated here, in pounds,
together with the but-
ter-fat analysis taken
at various intervals.
CURVES FOR THE EXECUTIVE
279
The days on which the
butter-fat analysis were
made are quite accurate-
ly indicated by the dots
on the butter-fat curve.
Figures for the milk pro-
duction each week are
given to hundredths of
a pound in the appro-
priate column above,
and the butter-fat anal-
ysis is given to one one-
hundredth of one per
cent for each date on
which the analysis was
made. The grand total
milk production for the
year of the test is given
at the foot of the col-
umn. Note the diag-
onal arrangement of the
two headings, "Pounds"
and "Per cent Butter
Fat". This diagonal
arrangement is a .con-
venient one as it is easy
to read and refers to
each of two columns of
figures, one column ver-
tical and the other hori-
zontal.
A card for each cow
as indicated above is
worth while in a modern
dairy. Individual rec-
ords are fundamentally
necessary to efficient
operation . There is such
a wide variation in cows
that unless they are care-
o/o)
oof,
o
"9
SZ9
Z90>
Fig. 214. Milk Production of a Cow by Months for Five Years
Since a card 12 inches long is necessary in order to show figures for fifty-two weeks in one year, we can also use a card 12 inches long for five years bys
months. Having five years on one card saves handling so many separate cards, but there is a disadvantage in that curve cycles for different years
cannot be so easily and ac "urately compared as with the vertical arrangement of yearly cards seen in Fig. 207
v
•* .
*—
*
^
/
T
•^
7
r
j
/
J
O9"
osg
\ Li9
e*g
?<?//
ooo/
0
$9i
I 90 //
^ 4 SO 6 obi/
\ 009
ooz
Sj SS9
^ OSb
A '*"
1
v"
s
•** .
-— .
*
/^
' ?
"
]
^
7
*
i
/
j
I
\
— . .
*
/^
O-
0-
/
*
r
y
\
/
\
/
**
^
~~- •«
~— .
*
x
i ?
*
1
/
/
™ * '
V*
^.
^ **
'-~
0CZ
*
^
?
^^
^^^
^
/-i/
r/o
/
Z/4
/
> Q
n/s/oi
oi/oe/b
bo/f/oi
90/h/OI
UJOq 39 A 1 DO
f
280
GRAPHIC METHODS
bfl
CO
o
4^
C/3
0
.3
8,
5 2
C3 0)
S N
o ^
a 3 1§
•3 r+ ~ ™
*8 jr
. «)
co >
*s g
£ £»
VB Ji
K, O *J f
'to « o *
M .9 rt
L. O CC^
^O
o>
t
J^
•8.5
•*•* ~^
u o
<tf .,
d
o
H
4>
—
•<->
CO
o
O
•a
a
o
b
^3 33
en o
^^2
fully watched there
are certain to be in
every herd cows whose
milk production is far
below the average.
Individual records of
each cow are now be-
ing kept regularly by
up-to-date dairies,
and any cow that fails
to give a definite mini-
mum of milk with a
definite per cent of
butter-fat is sent to
the butcher. Curve
cards are a conven-
ient means of record-
ing the output of each
cow in such form that
instant comparison
between cows is pos-
sible.
In Fig. 214 a rec-
ord for one cow for a
period of five years is
shown on a 4-by-12-
inch card. As the
card 12 inches long is
necessary for weekly
records, a card of the
same size can be used
conveniently to show
five years by months
instead of using five
separate 4-by-6-inch
cards, one for each
year. In Fig. 214,
the figures at the top
of the card show the
CURVES FOR THE EXECUTIVE 281
milk production each month and the total milk production for each
calendar year. The notes in the left-hand margin show the dates on
which calves were born.
In Fig. 215, also, curves are plotted on a card for five years by
months. In this case there was no hope of getting the cost per ton
below 50 cents, and the scale was accordingly so chosen that it began
at 50 cents instead of at zero in order that fluctuations from month
to month might be more carefully observed. As the zero line was not
shown on the card, the wavy line was drawn at the bottom of the
ruled portion, indicating clearly to the reader that he must not inter-
pret the curve as though the bottom were at zero.
When using an arrangement showing five years by months on one
card, considerable mental effort is necessary to get a clear interpreta-
tion of the fluctuations in the curve from year to year. In Fig. 215
certain peaks in the curve appear to have somewhat similar shape.
Thus the peak for 1908 looks like the peak for 1907 until closer ex-
amination shows clearly that the low point for 1908 was in July,
while the low point following the peak of 1907 came not in July, 1907,
but in January, 1908. The waves themselves, although of somewhat
similar shape, have peaks at entirely different times, the peak for 1908
being in February and the peak for 1907 in April. The foregoing
examples may serve to point out the mental effort necessary in read-
ing horizontally if the danger of misinterpretation is to be avoided.
If the curves for these same years 1907 and 1908 were plotted on
4-by-6-inch cards, and one card placed above the other as in Fig. 207,
there would be no possibility of error on the part of the reader. The
eye would follow the vertical lines and see at once that there was no
great similarity in the two waves. Having five separate cards causes
the reader to take more time in handling cards in order that he may
save mental effort and avoid error in interpreting the yearly waves.
Having five years on one card saves handling the cards, but it takes
more mental effort to be accurate in reading the curve horizontally.
The choice between five cards of one fiscal year each and one card
for five years must rest with the judgment or the habit of mind of
each individual person.
It sometimes happens that the seasonal wave in a curve is almost
completely obscured by the tendency toward a very great increase
or decrease in the business. Conditions may give so large an increase
in volume of business in any one year as to more than offset any de-
282 GRAPHIC METHODS
crease due to a seasonal period of slackness. The manager may think,
therefore, that his business is not affected by seasons, when in reality
the seasonal changes are very great. The extent of these might be
very evident if, for instance, a panic year should come along and
suddenly stop the upward tendencies in the curve resulting from
the rapid increase in the size of the business. This is an important
point for any small business to watch, for it may involve bankruptcy
to assume that the particular business is not affected by slack seasons
of the year such as affect most businesses. Fig. 211 gives an example
of a curve in which a large amount of seasonal fluctuation might be
easily seen if the rapid increase in the business did not make the up-
ward trend from increased sales greater than the possible downward
trend due to seasonal changes.
It is often necessary to compare curves for entirely different things.
For instance, it is desirable to compare expenses with sales. When
sales increase expenses per unit should decrease, and vice versa. Tre-
mendous saving can be made in most large manufacturing plants by
carefully watching the curves for the unit expenses and the output.
Something is usually wrong in any department in which expenses
per unit increase at the same time that the output curve goes upward.
When the amount of work done is fluctuating greatly, as during
periods of business depression, the executive may often get many vital
hints for the operation of his plant if he will simply make periodic
examinations to see whether the overhead-expense curves for each
department react in the manner which would be indicated by fluctua-
tions in the curves for direct labor or for quantity of output.
In making comparisons between separate curves there is a great
advantage in having a standard arrangement of the five-year cards
so that there may be no danger of comparing two curves for different
years when it is intended to compare for the same year. It is desirable,
as seen in Fig. 215, that all five-year cards should have the years
arranged by half -decades. One arrangement includes those years
ending in one to five inclusive, and the other arrangement takes those
years ending in six to ten inclusive. The person reading the curves
can then pick up any two cards relating to the same half-decade and
compare the curves instantly and correctly, simply by placing the
cards so that the edges coincide. If this half-decade arrangement
were not followed there would be five different positions in making
curve comparisons, and there would be grave possibility of frequent
CURVES FOR THE EXECUTIVE 283
error in that different years might be compared without the reader's
noticing that he was making an error. In starting a new curve on a
five-year card the curve should be started in the middle of the card
if the first year plotted happens to fall in the middle of a half -decade.
The half -decade arrangement should be carefully followed even though
it does not leave a portion of a card unfilled.
The fine-line curve running through Fig. 215 represents a twelve-
months moving average of the points on the heavy curve. If the
executive wishes to know the general trend of his costs, he refers at
once to this fine line and sees what the cost has been for the last twelve
months for which costs are known. In making up this moving average
(as explained in Chapter VI), one month is dropped from the addition
and another month is included in the addition, so that the twelve
months added are always the most recent months for which figures are
available. Note in Fig. 215 the degree of accuracy used in recording
the figures for the curves. Costs are known quite accurately in this
case and are recorded here to one one-hundredth of a cent. The moving-
average line shown above is a much simpler line than the curve line, for
the reason that the violent fluctuations in the heavy curve are largely
eliminated by the method of moving averages. The general rule for
smoothing a curve is that the number of points included in the moving
average should be the number ordinarily found in one complete cycle
or wave on the curve. This principle also was more fully discussed
in Chapter VI. In Fig. 215 the length of the wave is approximately
one year. It is accordingly good practice to have twelve points in-
cluded here in making up the moving average, so as to give as smooth a
curve as possible. If there had been a complete wave or cycle every
six months instead of once a year, it would have been desirable to use
six points in the moving average, rather than twelve points. The prac-
tice in many offices is to use the last twelve months in making up a
moving average, though it frequently occurs that a smoother curve
would be obtained if some other number of months were used.
As will be seen by reference to Fig. 91, points for a moving-average
curve are usually plotted in the middle of the horizontal space covered
by those points included in the moving average. In executive-control
curves such as are seen here, it seems desirable to make an exception
to the general rule and plot the last point on the moving-average curve
so that it falls on the same vertical co-ordinate line as the last point
included in the average. If the moving-average curve were made as
284 GRAPHIC METHODS
in Fig. 91 it would be following so far behind the periodic record curve
that the ordinary reader would not realize that the moving-average
curve is really up-to-date. For executive work, the object of a moving-
average curve is not so much to get a smooth curve as to show the aver-
age for the preceding year or other period of time considered. Under
these circumstances it seems permissible to plot the moving-average
curve as done in Fig. 215 instead of following the accepted method
shown in Fig. 91.
In the last portion of Chapter VII some of the disadvantages of plot-
ting curves on ordinary ruled co-ordinate paper were discussed. One of
these disadvantages is due to the great difference in fluctuation with
curves of small and of large numerical quantities placed near the bottom
and near the top of a chart. In order to overcome this disadvantage,
curves are often plotted on logarithmic paper. It seems desirable to
point out that curves plotted on the curve cards described here are
usually compared so that the disadvantages commonly found with
curves plotted on ordinary co-ordinate paper are largely overcome.
If only single curves are plotted on each curve card, and the zero line
appears at the bottom of each card, then curves on different cards have
approximately the same percentage scale. If two curve cards with
different numerical scales are compared the comparison is much more
accurate than would be the case if the two curves were plotted on a
large sheet of paper to the same numerical vertical scale. The fact
that the curves are all put into the same size of space on the curve cards
causes them to have somewhere near the same percentage scale of
height, even though the actual numerical scales may be widely different.
Having all curves on the curve cards thus gives more accuracy and ease
of reading than would be obtained if several curves were shown on
large sheets of arithmetically ruled co-ordinate paper with one curve
above the other to the same scale.
On the left-hand edge of each curve card shown in this chapter will
be noticed the word "Authorized" with a space for a date and initials.
When a new curve is added to the list of those curves which are regularly
plotted in any organization, the man who desires to see the curve periodi-
cally must put his initials and the date of signing on the left-hand
margin of the card. This is to show his approval of the general form
in which the information is given, and to authorize the expense neces-
sary in collecting data and plotting the curve, week by week or month
by month. A definite authorization, by which some one must sign his
CURVES FOR THE EXECUTIVE 285
initials in the manner described, assists greatly in preventing unneces-
sary clerical work, as it eliminates any curves which are not used
somewhere in the organization. The man who approves the curve
can be told just about what it costs to plot each curve. For instance,
if three thousand dollars a year is expended for the labor, materials,
etc., necessary in plotting all the curves in an organization, and there
are three thousand curves kept regularly, it can be seen that the ex-
pense per curve per year will be about one dollar. Therefore, if the
man should wish one hundred curves plotted for different data relating
to his department, he would be approving an expenditure of about
one hundred dollars per year.
At odd times before the end of any year the person who does the
curve plotting should begin to get titles and scales in place upon the
new cards, which will be necessary at the end of the year when the cur-
rent curves have reached the right-hand edge of the cards. As most
curves continue on the same basis as before, the man who has charge
of the plotting would take the new cards to those different men who had
approved the curves in the preceding year. If, during that year, any
change in departmental organization had occurred which would affect
the manner of plotting a curve or the facts which should be shown -in
any curve, the change would automatically be brought to light by the
man who must authorize the continuance of the curve. In large cor-
porations, department heads and officials change so rapidly that con-
tinual vigilance is necessary to weed out those records and clerical
procedures which are no longer of any use. The authorization plan
here outlined, if any man leaves a corporation, would automatically
give his successor an opportunity to consider how much of the curve
plotting should be continued on the basis formerly used. There is
always a great personal difference in the manner in which executives
desire reports prepared. The authorizing of curves periodically gives
each executive an opportunity to think the matter over and to have
data prepared in the manner which is most effective for his individual
use. In most organizations the president or the general manager would
be likely to have certain standard ways of assembling data and plotting
curves, since the chief executive officer must usually refer at some time
to each of the records of the different departments. The standards
of the chief executive would thus tend to prevent any freak methods
being introduced into the general curve-plotting scheme by any depart-
ment head further down the line.
286
GRAPHIC METHODS
Each curve plotted regularly is assigned a serial . number for con-
venient identification. This serial number remains the same year after
year, even though changes are made in the manner of assembling data
or in any other minor details affecting the curve. The serial number
is placed at the upper left-hand corner of the card, where it can easily
be seen when the cards are filed in. card-index filing cabinets. The cards
are identified by the number and year, as may be seen in Fig. 211 where
the three cards are 1910 191 i 1912. When two curves appear on the same
card, as in Fig. 215, they may be identified by the letters "A", "B",
"C", etc., placed on
the chart near each
curve, and any refer-
ence to the several
curves may be made
as4323A-1910,4323B
-1910, etc. When
five years are placed
on one card the last
year given is marked
in the upper left-
hand corner of the
card, as in Fig. 215,
to identify the card
and show that it
represents all the
data for the half-
decade ending in
that year.
Fig. 216. Each Curve Card Plotted Periodically Has a
Serial Number. A 4-inch by 6-inch Record Card is
Filed by the Curve Serial Number to Give the Com-
plete Information Necessary so that Anyone May
Know How to Collect the Data and Plot the Curve.
The Card, Shown Above, Refers to Curve 2678 Shown
for Three Years in Fig. 207 and in Fig. 208
It is not feasible or desirable to place on each curve card a title so
complete that it gives all the information concerning the source of the
data used in plotting the curve. It is better to use a fairly short title,
and then have all supplementary information given on a separate card
to which reference, if necessary, can easily be made. Fig. 216 shows a
4-by-6-inch card such as is used in conjunction with each curve card
regularly plotted. The number on this card corresponds with the serial
number on the curve card as will be seen by referring to Fig. 205 and
Fig. 207. If two or more curves appear on the curve card, a card like
that in Fig. 216 would have subheadings such as 2678A, 2678B, etc.,
all shown on the same card No. 2678. It will be seen that the informa-
CUKVES FOR THE EXECUTIVE 287
tion given on the card in Fig. 216 is much too lengthy to be included
as a portion of the title of any curve card. The information on the
record card is so specific that a new man in an organization should be
able to follow the card instructions and assemble all the data necessary
to plot each curve in the wrhole set.
Information cards such as are shown in Fig. 216 can sometimes be
simplified by expressing the information as a formula. Curve numbers
used in a formula may greatly simplify the method of expressing the
fact that several sets of data must be added and one total divided into
another total to obtain a desired ratio. Though information cards like
that depicted in Fig. 216 are used principally by the man who plots
the curves, they are filed in such convenient location that they may be
referred to by any executive who wishes to know the source of the data
plotted on any curve card, or who wishes to see just what figures are
included and what are excluded in making up any grand totals. The
use of the serial numbered information card gives full information in
condensed and easily accessible form.
CHAPTER XIV
RECORDS FOR THE EXECUTIVE
A GOOD executive has been described as a man who decides
quickly and who is sometimes right. Probably ninety per
cent of the answers :'Yes" or "No" given by a business
man are based on opinion rather than on fact. The trouble is that
the average executive cannot obtain and analyze facts quickly enough
to base his decision on them. He is forced to decide quickly and his
one hope is that he will guess "right".
The problems confronting the executives have grown, in the last
few years, to such an extent in volume and in complexity that it is
increasingly difficult to find men with endurance and capacity great
enough to match the jobs. The executives of our corporations, the men
who are mayors of our cities, and the men in active charge of the govern-
ment of our country are, without exception, the hardest worked men in
the world. The stoker heaving coal into the furnaces of an express
steamer has a better chance for long life than the man who accepts the
presidency of even our best managed railroads and industrial corpora-
tions. The stoker can at least sleep soundly at the end of his day's
work. The railroad president is likely to be kept awake wondering
whether his guess was a good one, whether his decision was "right".
The men now steering the courses of our big corporations are men
who have come up the line, step by step, through each department.
They know accurately the relation of every department to every other
department in their own company. They have available, also, a tre-
mendous fund of information as to what has been accomplished by their
competitors. The present executives of corporations are fortunate,
in that they have seen, in their own business experience, each of the
steps toward the greater division of labor and the consolidation of
executive control which have done so much to make economic produc-
tion possible by large-scale production.
288
RECORDS FOR THE EXECUTIVE 289
The present executives are extremely fortunate in that they had
an opportunity to develop themselves at the same time that their
jobs grew bigger. What are we going to do ten years hence, when execu-
tives who have had such thorough training have all retired or have been
killed off by the strain of the job? Where shall we find men with broad
enough knowledge and experience to decide, instantly and correctly,
each problem placed before them?
The answer is that the executive of the future will be forced to
depend on the analysis of facts which have been collected and arranged
for his instantaneous and continuous use. The executive of the future
will decide quickly, and, he will be more than "sometimes" right, be-
cause he will base his decisions on the analysis of actual facts. His
value as an executive will depend chiefly upon his powers of accurate
analysis.
Corporation directors are changing rapidly these days. Suppose
a newT director were to come into your corporation, what could you show
him of the history and present standing of your business that would
permit him to give an intelligent director's vote within a year of his
election to the board?
It is perfectly feasible to focus a whole business into records so
simple that a trained man could see, in half a day, all the important
tendencies well enough to give an intelligent director's vote. This,
too, without a spoken word of explanation from anyone. The records
themselves could tell the complete story in every detail if placed in
proper graphic form. It is the purpose of this chapter to show how
such a thing may be done.
Fig. 217 shows a standard 4-by-6-inch filing case used to file curve
cards and information cards. The right-hand drawer shows the 4-by-
6-inch cards filed with appropriate guide cards. In this particular
case, the guides give the names of branch houses by cities. The left-
hand drawer shows the 4-by-l 2-inch cards filed according to the loca-
tion of factories. As factory payrolls must be watched closely, weekly
records of the payrolls were kept for this corporation, though monthly
curves were found to be sufficient for the sales. There is no difficulty
in filing the 4-by-12-inch cards in a standard 4-by-6-inch filing cabinet.
The follow-up block in the drawer is placed 12 inches from the end of
the drawer, then the cards are filed lengthwise with a sufficient quantity
of blank cards at the back to keep all the cards in an upright position.
Of course a special filing cabinet 12 inches wide can be made if desired,
290 GRAPHIC METHODS
but it is not really necessary. In a cabinet like that shown in Fig. 217,
the original curve cards would ordinarily be filed behind the guide cards
showing the factory or selling-house locations, or behind guide cards
showing the names of departments in any large business. All the cards
for succeeding years would be filed behind the proper guide cards, with
the curve card for the earlier year at the front. Having the card for
the earlier year at the front instead of at the back permits comparison
of curves for different years with a very slight lifting of the cards,
and without any danger of the cards being put back in the drawer in
mixed order.
Information cards like those shown in Fig. 216 would be filed in
the same filing -cabinet. These 4-by -6-inch information cards are filed
by curve serial numbers, with appropriate numbered guide cards so
that any information card may be quickly located by its serial number.
As the numbered information cards are needed only for occasional
reference, they can be put in the back portion of a file drawer, leaving
the front portion of the drawer available for the curve cards more fre-
quently needed.
In checking up the condition of his business, the executive usually
considers it department by department. For this reason the original
curve cards should be filed by departments so that the complete history
of any department may be had from the cards behind the guide card for
that department. A large portion of the executive's work, however, in-
volves the study of his general business not by departments but by
functions. For instance, the executive may wish to know how many
employees he has in his whole business, and how many employees there
are in each department, if he is considering the departmental increases
or decreases which affect the total payroll. It is therefore desirable
that the executive should have available for instant reference a cross-
index of information which will show his whole business by function
instead of by department. Such a cross-index can easily be provided,
when curve cards are used, by taking a blue print of each curve card
and then filing the blue print by function, instead of by department.
In such an arrangement, there would be a complete set of guide cards
giving different headings, such as "Number of Employees", "Total
Sales", "Total Expenses", etc., with guide cards having suitable sub-
headings placed behind each one of the main guide cards. A blue
print of the curve showing the total number of employees in the corpora-
tion would be filed at the front of the division for employees. Back of
RECORDS FOR THE EXECUTIVE 291
this total card would be filed blue prints showing the employees in each
department of the whole plant. Thus, if a total card at the front
showed that the employees were increasing, the manager could refer
to each one of the department cards filed immediately back of the total
card to see in just which departments there had been an increase during
the last month, and in which department there had been a decrease.
Fig. 217. A Standard 4-inch by 6-inch Filing Case Is Used for the Curve Cards.
Cards Twelve Inches Long Can Be Filed Lengthwise in a Drawer without In-
convenience
Guide cards separate the curve cards by departments. If desired, blue prints can be made from each curve
card and the blue prints filed by expense-account numbers, as a cross-index of the data on the white
cards which are filed by departments
In a similar manner, the blue print showing total expenses would have
filed back of it cards showing the detailed expenses by departments
or by account numbers. If expenses had increased the manager could
refer to the departmental or account-number cards and see just which
departments or accounts were responsible for an increase or decrease
in the curve giving the total. The cards in a large business would
be filed by expense-account numbers, with the total card referring to
any expense account for the whole business filed at the front of each
group of cards giving the figures for that expense account by depart-
ments. Thus, in a manufacturing plant, the card showing the loss
292 GRAPHIC METHODS
from spoiled work as a percentage of the total payroll could have filed
back of it cards showing the percentage loss in each department. If
the spoiled-work curve for the whole business should go up in any month,
the manager could see instantly in which departments the percentage
of loss had increased and in which the percentage had decreased. Let-
ters could be sent to the foremen of the departments having bad records,
calling their attention to the bad showing made.
The cross-index of curves, obtained by filing the cards according to
function or by expense-account number instead of by department, is
of tremendous importance to the busy executive. This feature alone
may save a large amount of his time by making necessary information
more accessible, and by affording information which may show leaks
in his business that he would otherwise never know to exist. In a
business of any size the cost of making one blue print each month from
each original curve card is almost insignificant. The guide cards
showing functions or account numbers remain useful year after year, and
it is necessary only to discard a blue print for each card each month and
to substitute the latest blue print made from the original curve card
after a new point has been added. Having the original cards filed
by departments and the blue prints filed by function or account number,
the manager may instantly consider his business from whichever point
of view he desires. He may study the whole operation of a given
department, or he may study one function or expense account in its
effect upon his business as a whole.
Practically every company which does an annual business of
$1,000,000 or more would find it a paying proposition to have a room
reserved in the office as a general record or information department
regarding all the facts of the business. Though such a room might
be combined with a technical library for books relating to the particular
art or industry in which the company finds its field of operation, it is
advisable to have the amount of furnishings in the room limited so
that there may be no likelihood of valuable confidential papers being
lost or misplaced. Such a room really needs to have no more furniture
than filing cases like those shown in Fig. 217, a large table, and a draw-
ing table or a flat desk for the man who plots curves.
It would be the function of a man having an office like that described
to collect for the business all the data and facts which would be of any
assistance to the executive, the officers, or the department heads.
Most of his work would relate, of course, to getting data and plotting
RECORDS FOR THE EXECUTIVE 293
curves for all the operating reports of different departments of the busi-
ness. The operating reports regularly furnished by the accounting
departments of the business would be gone through carefully, and
figures transcribed from these reports to the curve cards mentioned
previously. There could also be in the record room a series of maps,
large wall charts in the form of curves, and perhaps loose-leaf books
or large vertical card files for cumulative curves such as are shown in
Fig. 134. Since the information contained in this room is practically
a history of every phase of the business, it would be desirable to have
the room enclosed with fire-proof walls and fire-proof doors and equip-
ped with fire-proof file cases and furniture so that the destruction of
the records by fire would be absolutely impossible. As good light is
essential in such a room, large windows are necessary. The windows
can ordinarily be sufficiently protected against fire by using polished
plate glass reinforced with wire to prevent breaking of the glass from
fire in adjoining buildings.
The title given the man who does the work described is really not
important. Ordinarily, in a large corporation, he would be ranked as
assistant to the president, as he should report only to the chief executive
officer in the particular office in which he is located. He could, if
desired, be given the title of chief of the record department, or, in a
larger business where much specialized information is sought from
outside sources, the title of "statistician" might be justified. In the
work of most corporations it would soon be found desirable to have a
man of the type described collect and record, for convenient use, data
from sources entirely outside of the business itself. Most companies
have to buy large quantities of raw material which fluctuates greatly
in price. To assist in making decisions relating to purchases, it would
usually be found desirable to have curves plotted for the chief materials
entering into the finished product, such as pig iron, copper, tin, zinc,
cotton, lumber, coal, etc. Very desirable information could also be
obtained concerning the business conditions of the country as a whole.
Since practically every business is affected by the general waves of
financial prosperity and depression, a good man in this position could
be of great assistance to the chief executive, by carefully studying
some series of curves (which might, after long experience, prove to be
the best barometer available) to indicate changes for better or worse
in the general financial conditions affecting the particular business in
question.
294 GRAPHIC METHODS
In a business of ordinary size, the yearly outlay for an office like
that described and a man to run it would be comparatively small. It
would probably be best to get a young man graduated within a few
years from one of the technical schools, or from one of the schools of
business administration now established as separate departments in
several of the large universities. If a man of the right type were told
that he would report directly to the chief executive, and that he would
have a confidential position with complete access to the records of every
department of the whole business including both manufacturing and
selling, he would be quite willing to start the work at a reasonable
salary, knowing full well that the opportunities given would soon per-
mit him to demonstrate his ability. A recent college graduate could
be obtained for $20 or $25 per week, as he would see for himself that
there would be chances for him to make himself worth much more inside
of the first year or so.
A man starting a record department of the type described would
at first find his chief work in getting records for a series of years so
that comparisons would be possible. In most corporations it is extreme-
ly difficult to get any kind of good records further than two years back,
because of constant changes in personnel and changes in accounting
systems without any reliable notes to tell just what these changes were
and when they were made. In large manufacturing companies, sub-
divisions and changes in the expense accounts are likely to occur as
new departments are added or as new men of different training in ac-
counting come into control of the accounting procedure of the company.
After the back records have been fairly well tabulated and plotted in
the form of curves, the work of keeping the curves up to date would
be comparatively simple. One man can add one more point monthly to
several thousand different curves, and do also a certain amount of
the clerical work involved in making up ratios, grand totals, etc. If
a record file of curves like that showTn in Fig. 217 is once made thorough-
ly up to date, for any business, it is easy to keep it up to date with only
routine work such as any man of even ordinary mental caliber can do.
Information cards 4-by-6-inch, such as are shown in Fig. 216, explain
every step of the work required in plotting any curve, and even a new
man just out of college would be able to follow the instructions well
enough to take charge of a record system which some one else started.
Thus, if it is desired after a year or two to promote a man who has built
up a record system of this kind, it would be quite easy to have him break
RECORDS FOR THE EXECUTIVE 295
in a successor so that there would be no change in the methods of col-
lecting data and plotting curves. This possibility of taking on a new
college graduate every few years permits having an excellent record
department, even for a small-size business in which it would be thought
undesirable to spend more than $3,000 or $4,000 a year to cover the
total yearly departmental cost.
It should be a strict rule for a record department of the type de-
scribed that no original papers shall be taken from the room. The rec-
ord department should be in a quiet place to which the president or
any other official may retreat to get completely away from the distrac-
tions which are common in his own office because of the telephone and
constant visitors. In the record room the executive would be free to
concentrate his whole attention on the records of what his business
has been doing in the last weeks or months, so that he may be able to
formulate plans for the future. Though the arrangement of the files
in the record room would be well known to the executive, so that he
could lay his fingers instantly on any desired curve or other record,
the chief of the record department would be at hand most of the time
so the executive could send word ahead to have certain curves or other
records laid out for instant reference when he arrived. To save time
the executive should not be required to put back into the card files
the curve cards which he has taken from any file drawer. By using a
large table the executive could simply push to the other side of the
table any cards which he may have laid out for careful comparison.
The man who has charge of the room can later put the cards back in
the files. There is an advantage in having one man put all the cards
back in the files, as in this way there is less chance of the cards being
misplaced in the file than if several different executive officers were to
use the cards and themselves put the cards back. It should be stated
here that in the ordinary use of curve files such as are shown in Fig. 217
an executive would not need to remove the cards from the drawer. He
would simply turn the cards over one at a time, raising any card of
special interest about three inches to look at it, but not removing it
sufficiently to cause any danger of restoring the card in a wrong position.
It is only when cards for a series of years are taken out and laid down for
comparison with some other series of cards that there is any necessity
for removing the cards from the drawer.
The Westinghouse Electric and Manufacturing Company of Pitts-
burgh regularly plot about four thousand curves which record the
296 GRAPHIC METHODS
activities of all departments of the business. The majority of the curves
have one more point added each month, but some of the curves are
on a weekly basis. Day and Zimmermann, of Philadelphia, are plotting
a total of about eight thousand curves, most of the curves on a
cumulative basis somewhat as shown in Fig. 134. In order to allow
space enough for a cumulative curve (which naturally takes up more
room than a curve plotted on a non-cumulative basis), the curves are
plotted on cards 8J^ inches by 11 inches, and these cards are filed ver-
tically in a tray desk so that a man sitting at the desk can instantly
lay his hand on the proper card for any one of the eight thousand curves.
Guide cards are of course used to make card location easier. To pre-
vent cards being replaced at some wrong position in the file, Day
and Zimmermann have worked out the clever scheme of notching in a
similar manner the tops of all cards which are filed in any one division
of the file. When cards are filed one after another the notches of indi-
vidual cards form a groove in the group of cards. If any card should
be filed out of place it would break the continuity of the groove and
would instantly be noticed. In using the notched-card scheme two
notches may, if desired, be placed in the top of each card, thus permit-
ting many more group combinations than would be possible if only one
notch were used. The notches may be cut with a special instrument of
rather simple construction so as to insure their uniform spacing right
or left from the upper corners of the card. A notch in the form of a
segment of a circle is the most satisfactory.
In order to keep the general rule that original curve cards shall
not be taken out of the record room, it is well to provide means by
which blue prints can be made quickly from any curve card. In a
business of reasonable size, blue prints may easily be made with a
small-size printing frame and sunlight printing, if the record room is
located on the southern side of the building where there is sunlight most
of the time. In large businesses electric blue-printing machines are a
part of the regular equipment of the drafting office. If the drafting
office is not near the record room, however, it may be well to equip the
record room with an electric blue-printing machine and a small washing
tank, so that blue prints of each card may be made without the neces-
sity of taking confidential record cards out of the room. Photographic
processes for copying records have recently been much improved. A
machine called the photostat makes black and white copies quickly
without the expense of glass negatives. With a blue-print machine or
RECORDS FOR THE EXECUTIVE 297
a photostat in the record room, it would be a very simple matter to
copy periodically the complete current set of curves so that the cross -
index of cards by function or account may be provided for the execu-
tive, as described in the preceding paragraphs.
The plan suggested for a record department sounds much more com-
plex than it really is. In considering the space and expense necessary
for such a department it must be borne in mind that the time of the chief
executive of a modern corporation is of a great value — almost beyond
computation. The value of the president's time in a large corporation
cannot be figured out on the basis of his salary, for it is certainly true
that the executives of large corporations receive salaries much less
than the value of their services to their corporation. A single "yes"
or "no" decision of the corporation executive usually involves a gain or
loss in the earnings of the corporation greater than the executive's
salary for a whole year. Anything that can be done to give the presi-
dent and the other executives better and more quickly available in-
formation on which to base decisions is justifiable and should be in-
stalled practically without regard to cost.
In a large office it will be found desirable to give a number of
department heads access to the record room. As no one would ever be
admitted to this room except the chief executive, and department heads
who were given written permission by the chief executive, there would be
no danger of confidential information coming into the hands of outside
parties. As it may not be desirable to have department heads in a
business know anything about the finances of the company as a whole,
or anything regarding the records of departments other than their
own, it may be best to have the curve cards filed in several drawers with
a separate drawer for the cards relating to the work of each department
head. If the drawers are equipped with spring locks, each department
head could have a key to his own drawer, yet it would be impossible
for him to go through the records of departments other than his own.
The chief executive would, of course, have a master key to all the draw-
ers, so that he could compare the records of one department with the
records of any other department whenever he desired. The presence of
the man in charge of the record department would in itself tend to
keep minor officials from going through the cards relating to bank
deposits, earnings, etc., for the corporation as a whole. There would
necessarily be times when the head of the information department would
not be in the room while minor officials were there, and the expedient
298 GRAPHIC METHODS
of locking up the summarized control curves for the whole corporation
is therefore mentioned here as a possible safeguard.
Directors and executives change quite frequently in large corpora-
tions. When a new man comes into a corporation as an executive or a
director, the value of his service to the corporation is at first practically
nothing, and he may even for a while be considered a handicap to the
corporation in that it is necessary for men who have been associated
longer with the corporation to spend a great deal of their time in explain-
ing to the new member the facts relating to the various departments and
to the present scope of the business. This information is generally
passed on from man to man by word of mouth. Usually there is no
written statement giving in condensed form a bird's-eye view of the
whole history and present field of the corporation. Broadly, it is now
almost impossible for any new director in a corporation to give an
intelligent director's vote on any proposition brought up within a year
after he has joined the directorate.
It will not be long before every man holding the position of a corpora-
tion director or a corporation executive will be able to read, quickly
and intelligently, simple curves and figures like those combined on the
curve cards here. With a card-index file of curves and a record depart-
ment like that described in this chapter, it should be possible for any
trained man coming into a corporation as a new director or new official
to give a fairly intelligent vote after only half a day's study of the
curves, and this too without having spoken a single word to anyone.
If the record department and the curves are properly kept, the whole
situation would be shown on the face of the cards with far more clearness
than it would ordinarily be possible to give by words alone, even if
the whole history and present status of the corporation were told.
Consider the value of a record department like that suggested, if
such a department were part of the equipment of the mayor's office of
any city. The department could be maintained continuously by civil-
service employees who could keep the records in standardized form year
after year, no matter what shake-ups there might be in political parties
and in spite of the numerous changes in personnel usual when one set of
city officers follow another with great rapidity. In municipal work
there would be no necessity for keeping any except the original curve
cards under lock and key, as all the information would be public
property and, of course, available to properly authorized persons. It
would certainly make a great difference to any new mayor if he could
RECORDS FOR THE EXECUTIVE
go to a record room and study a set of curves showing, for instance, the
total number of men in the employ of the city year after year under
different administrations. He would be able to see over a period of
years the number of men in each city department such as fire, police,
street-cleaning, etc., together with the average rate of pay. He would
also have complete information over a long series of years regarding
taxable property in the city, tax rates, total population, death rates,
etc. All this information would be available instantly, not only to the
mayor but to each member of the council, who might apply to the record
department very much as he would apply to any good reference library
when in search of information. The only rule necessary would be
that no curve cards should leave the room. To safeguard information
files to which numerous councilmen have access, it would be wise to use
only blue prints in the open files, keeping the original cards in separate
locked files, available only to the man who plots the data on each card,
point by point, as information is received. Councilmen, civic organiza-
tions, newspapers, etc., wanting copies of any record card should
be able to get blue prints or photographs at a nominal charge of say
ten cents per card copy. The New York Public Library is successfully
working a plan by which photographs of any page of any book in the
library can be provided to readers in a few hours at a cost of only
twenty-five cents per page. A similar plan could be used for the sug-
gested copies of official curve records.
Progress in the government of the world, and especially in the
government of cities and of industrial corporations, has been greatly
retarded by the fact that the only information available to executive
officers has been provided to the executive in the form which is most
convenient for the use of the accountant. It is, of course, necessary
that records should be kept accurately from the standpoint of good
accounting, and the author has no complaint to make of accounting
methods in so far as accuracy is concerned. It is not, however, right
that executive officers who must determine policies and who must make
instant decisions should be forced to base all their decisions on
information provided to them only in the form of the accountant's
standard arrangement of balance sheet and operating statement.
The accountant must necessarily take a bird's-eye view of the
whole business from time to time, so that he may see how all the com-
ponent parts add together, to make certain that he gets a balance.
The result is that the accounting officer usually makes up a periodic
300 GRAPHIC METHODS
report, in which he gives at the end of any month or at the end of any
year a complete bird's-eye statement of the status of the business
at that particular time. Because of the nature of his problems, the
executive's mind must necessarily work in a manner absolutely dif-
ferent from that of the mind of the accountant. The executive does
not often want a bird's-eye view of his whole business at any one
period of time. What the executive must have is a cross-index of the
accountant's information, so that he may see over a long period of
time the whole history of any portion of his business. Most managers
are forced to work from the accountants' monthly statement, and
their procedure is accordingly to go through the separate operating
statements for several months and take off on scratch pads the figures
for the items in which they may be particularly interested at the
moment. These figures may have to be added together in order to
compare a certain number of months this year with the same months
of last year. This work not only takes the time of the highest paid
man in the organization, but the hasty scratch-pad figures are likely
to contain errors. It is absurd that executive officers should be forced
to make their own cross-indexes of the accountant's statement, and
not only make these cross-indexes but make them while holding the
long-distance telephone or at other rush times when seconds are
important.
The information as it comes from the accountant's office should be
passed to the man in the executive department whose function it is
to provide information for the executive by cross-indexing all in-
formation from the accountant's reports and putting this information
in the form of curves. The accountant's report would, of course, be
filed carefully for future reference purposes if reference is ever neces-
sary, but for the purposes of the executive the curve cards with the
figures they contain are sufficient. Not only is the information for
any subject shown on the cards as a curve over a long period of time,
but the actual figures of the accountant's report are visible in such
manner that they may be found instantly and quoted directly from the
curve cards without having to refer back month by month to the
original figures in the accountant's report.
The manager or chief executive of any business using curves in
order to keep in close touch with all departments will find that he
needs a liberal education in logic to enable him to draw the correct
conclusions quickly from the large number of facts available. There
RECORDS FOR THE EXECUTIVE 301
are certain general principles which are gradually being recognized,
and which within the next few years will doubtless be well enough known
to classify and make available for the executive's use. At present,
however, each executive must work out for himself his own means
of recording data and of determining policies in operating his business.
An example showing some of the difficulties involved in correct inter-
pretation is one concerning overhead-expense ratios. Some managers
consider the ratio of indirect expenses to the direct labor in any de-
partment of a manufacturing business as an infallible barometer by
which each department of the business can be run. They little realize
the absurdity of paying too much attention to overhead-expense
ratios and the danger to the business of using overhead-expense ratios
as a yard-stick by which to measure accomplishment. In this par-
ticular case, that of a large manufacturing plant, a new department
manager changed the manufacturing methods so radically that he
was able to produce an increased output with less than half the former
payroll for direct labor. The expenses for the foremen, clerks, sup-
plies, etc., in the department remained about the same as before.
Because of the reduced amount of direct labor the overhead-expense
ratio was of course doubled, much to the astonishment of the chief
executive, who accordingly considered this department as the worst
managed in his whole works. This executive had been running his
plant for so many years on the expense-ratio basis that the new de-
partment head found it almost impossible to convince the chief ex-
ecutive that the department was making money more rapidly than
ever before, even though the overhead-expense ratio had doubled.
The overhead expense itself had not increased, and the ratio was
doubled simply because the amount of direct labor had been de-
creased.
It is perhaps worth while to point out here that there is danger
in giving too much information and too many facts to executives
of small brain capacity who do not know how to use their authority
intelligently. Curves such as those described in this and the preceding
chapter, placed for the first time in the hands of the executive who
does not know the technology or the general underlying principles
of the business which he controls, are likely to prompt such a narrow-
minded director to send out a regular deluge of letters unjustly crit-
icising the actions of his subordinates. There is a possibility that a
small-caliber man in the manager's chair may send out too much
302 GKAPHIC METHODS
destructive criticism and not enough constructive criticism. If such
a misfortune should occur it would cause every department head in
the organization to withhold information and consider the whole
curve-record system as a new form of diabolical torture. Curves are
not intended to give any chief executive an excuse to "jump on " any de-
partment manager or foreman. The curve records are intended only
to point out those danger points at which construction work is needed.
An executive of the right type will soon realize as he uses the curves
that he must do the constructive work himself, and that the curves
will really have more effect in changing the procedure in his own
office than in changing the detailed routine in the departments of
his various subordinates.
One of the first tasks confronting any modern executive is that
of training, on the one hand, his board of directors and executive
committee, and on the other hand, his various department heads and
their subordinates, to read curves accurately so that the facts pre-
sented may be intelligently grasped and applied to the benefit of the
business as a whole. It is unfortunate that so many men serving
to-day on boards of directors and in executive positions of large busi-
nesses are not able to read even the simplest curve with any real
grasp of the facts portrayed. Engineers and other trained men who
have real facts available are tremendously handicapped in presenting
the facts if it is not feasible to use the graphic method of presentation.
A man prepared to show his data in the form of curves, for example
like Fig. 157 or Fig. 159, feels that he would have an almost hopeless
task to convey the vital facts if only spoken words might be used.
The writer ventures to predict that within ten years practically all
corporation directors and executives will be able to interpret curves
with satisfaction to themselves and with great benefit to their business.
The executive who cannot read curves will in the near future be the
exception rather than the rule.
If any general manager will take the trouble to train his department
heads to read curves and will then supply to them curves showing the
facts of his business, he will be tremendously repaid in the interest,
enthusiasm, and real progress toward improvement which will be
aroused in his men.
It is possible to use a reflecting lantern like that pictured in Fig.
218 to show on a screen the curves from the curve cards described in
Chapter XIII. Lantern slides are not practicable when frequent meet-
RECORDS FOR THE EXECUTIVE
303
ings of department heads must be held. The expense of making
lantern slides each time a new point is plotted on each curve would be
too great for even the largest corporations. Another disadvantage of
using lantern slides is the impossibility of getting slides made quickly
enough to represent always the latest points plotted on the curves. By
using the original curve cards directly in the reflecting lantern there is
always a certainty that the picture shown on the screen represents the
very latest data which are available in curve form. When these curve
cards are used in a reflecting lantern a simple slide carriage is made
Fig. 218. Reflectoscope as Made by A. T. Thompson & Co., Boston, Mass.
Lantern slides may be used as shown at the top of the picture. The stand holding the book may be replaced
by a simple carriage arranged to take the 4-by-6-inch and the 4-by-12-inch curve cards. The very
latest data from the file shown in Fig. 217 may then be instantly reflected onto a screen for use in a
meeting of the department heads of a business.
to replace the stand holding the book in Fig. 218. As the card is laid
down flat in its natural position and in plain view of the operator, there
i3 no likelihood of cards being put into the machine incorrectly. If a
carriage about two feet long is used, the carriage may be moved
alternately from right to left, and while one side contains the cards
which are being reflected on the screen, the other side may be loaded
with the cards next desired. On account of its length the carriage
will hold curve cards for several succeeding years. By pushing the
carriage slowly across the lantern the fluctuation in any curve may
be shown for as long a series of years as may be desired. Simple spring
clips on the carriage may be used to hold the overlapping cards in their
304 GRAPHIC METHODS
exact position. Not only are the curves themselves shown on the screen,
but the whole face of the card is seen so that the figures for any points
on the curve which are of special interest may be read directly from
the screen.
If the information or record room is large enough to serve for holding
conferences the lantern and the screen may be installed permanently
as part of its equipment. Ordinarily, however, it will be found best
to have the record room more private than any room used for general
conferences can be made, and the lantern would be part of the equip-
ment of the conference room rather than of the record room. With this
arrangement it will be necessary to take the curve cards from the record
room to the place where the lantern is installed. The file for the curve
cards (see Fig. 217) had better be equipped with spring locks so that
there wrill be no danger, when the file is carried, of drawers slipping out
and spilling the cards. A rod arrangement is never desirable with such
cards as these, for the rod would spoil the bottom portion of the card
and would also make it impossible to lift cards out for quick reference
or comparison. Brass handles on the sides of the file case would make
it easy to carry the case to the conference room. There, on a table
beside the lantern, the cards in the file case w^ould be available for use
almost exactly as lantern slides are used with the ordinary lantern. In
fact, the arrangement of the cards is even more convenient than the
usual arrangement of lantern slides in that the cards have a guide index
so that any desired card may be instantly located.
An executive who wishes to have a meeting of his department heads
need not make any very definite plan before the meeting begins as to
what cards he is to show on the screen. He can start talking to his
men, and, at pleasure, ask the lantern operator (ordinarily the statis-
tician) for any set of curve cards which may be of interest to him at
the moment, or which may be referred to at any time during the dis-
cussion. The use of curves on a lantern screen in the manner suggested
would entirely revolutionize the meetings of the department heads of
a business, or the meetings of branch-house sales managers. In sales
work especially, the use of the various cards would make it possible to
show the whole assembly the recent records made by selling houses in
the different parts of the country. The cards for those houses which
made particularly good records could be shown, the records could be
commended, and conclusions could be drawn as to how the success
had been attained. Records for the less successful houses could also
RECORDS FOR THE EXECUTIVE
305
Fig. 219. Curves on Swinging-leaf Display Fixtures Used for Ready Reference in
the Office of Day and Zimmermann, Philadelphia. Each Leaf May Be Easily
Carried to a Desk when Additional Points Are to Be Plotted on the Curves
This same type of display fixture is often convenient for showing pin maps of different territories
be shown, with comments by the sales manager giving his own sugges-
tions and asking for suggestions from the other branch-house managers
present.
Reflecting lanterns can be used at directors5 meetings as soon as
corporation directors know how to read curves. By using the lantern,
the president could show facts relating to the business much more
rapidly, much more clearly, and with greater accuracy than would be
possible with any spoken words. The showing of curves would give
the directors a chance to check the president's statements so that there
would be less danger than at present of a corporation president so
choosing his words that, though the words might be strictly truthful in
themselves, they would be over-op timisticT because they did not tell
all the truth. The presence of the whole file of curve cards immediately
beside the lantern would enable any director to call for facts relating
to any phase of the business on which he might desire information. The
use of these curve cards, and a lantern, would permit a properly educa-
ted set of directors really to direct the business for which they are
responsible to the stockholders.
306 GRAPHIC METHODS
It is sometimes desirable to have the chief facts relating to a business
plotted on wall charts which are instantly visible in a conference room.
Fig. 219 was photographed in the record room which adjoins the direc-
tors' room of Day and Zimmermann, of Philadelphia. On the swing-
ing-leaf fixtures a series of curves are plotted giving all the salient
facts relating to a group of public-service corporations. Though this
type of wall chart is in many cases desirable, there are limitations to<
the use of wall charts because the number of charts cannot be suffi-
ciently increased to give all the detailed information which is usually
necessary. Wall charts are suitable chiefly to furnish summarized
information to directors or other men whose time is limited or who come
to an office only at rare intervals.
Wall exhibits of curves can sometimes be used with satisfactory
results if special care is taken to draw the curves on a very large scale
and arrange them on all four walls of a room. A prominent financier
of New York City is said to have a large room, on the top floor of his
residence, where the walls are completely covered with curve charts
on which points are plotted as rapidly as data can be obtained. This
man is so limited for time that he keeps in touch with general financial
conditions by referring to the charts in this room for only a brief
time each evening. He disappears to his reference room to meet
his private secretary immediately after dinner. In the center of the
room is a revolving desk chair with an ash tray fastened to one arm.
For the length of one cigar the financier sits in his chair slowly re-
volving the chair until he has covered the information given on all
of the wall charts, perhaps, if necessary, asking a few brief questions
of his secretary. Though very little of the financier's time is taken,
he is able by concentrated thought on the facts shown by his wall
charts to keep in full touch with world finance and to map out his
own plans for future operation.
CHAPTER XV
THE annual report of a corporation is usually mailed to each
stockholder. The report, as commonly gotten up, contains prac-
tically nothing except a brief statement by the president in
regard to the last year's business, together with the balance sheet
and operating statement furnished by the accounting officers of the
company, and perhaps an audit by some firm of certified public ac-
countants. The report sent to a stockholder is essentially in that
form necessary for the auditor to check the financial figures and to
certify to their being in balance and correct.
Though the balance sheet and operating statement, with the letter
of approval by the certified public accountant, are necessary and de-
sirable, they do not contain, in themselves, the information most
desirable and most intelligible to the average stockholder. What the
stockholder needs most is a report from which he can make comparison
with preceding years. The bankers and large investors who can pre-
serve in their files annual reports of a corporation over a long period
of years probably number less than one per cent of the total number
of stockholders to whom the annual reports are sent. It is only in
very large, well managed offices that a file of corporation reports is
made so that a complete set of reports for a long period of years is
available for comparison with any new report which may be received.
The average stockholder cannot preserve his annual reports from year
to year in such manner that he can lay his hands on the earlier reports,
and thus compare the last report with the record of preceding years.
Even if every stockholder should have some yet uninvented type of
filing system by which everything is preserved and everything can be
found instantly when needed, that would not solve the problem. Stock-
holders are changing so rapidly that, of the total number of stockholders
to whom reports are sent in any one year, a comparatively small percent-
307
308 GRAPHIC METHODS
age have been stockholders for more than two or three years. Because
they have not been stockholders for any length of time, they cannot have
available the annual reports of earlier years to compare with any annual
report just received. The only way a new stockholder can possibly
determine whether he wishes to buy some more stock or sell what
stock he already has, is to hunt up some other stockholder or some
banker who may happen to have a file of the annual reports over a
period of years. Assuming that a complete file of annual reports can
be found, most stockholders, if left to their own resources, would be
hopelessly confused in trying to reach any correct basis for analyzing
the figures. Each stockholder would have to take a sheet of paper
and copy off, into different columns for various important items of
the operating statement and balance sheet, figures for a number of
years so that the figures for different years could all be seen at one
time and compared. This means that each stockholder would have to
make practically a cross-index of the most important data contained
in a series of annual reports in order to study the different phases
of operation independently. Even if the stockholder should know
how to make such a cross-index properly, there are very few stock-
holders who would be willing to give the time and the mental effort
requisite to make a tabulated comparison of the kind necessary.
The absorption of good securities by the public has increased in
the last ten years at a tremendous rate. The Wall Street Journal
has compiled statistics of the stockholders of the larger railway and
industrial corporations showing that the numbers have grown as
follows :
1901 227,000
1906 431,000
1911 865,000
1913 1,250,000
Mr. Samuel Rea, the president of the Pennsylvania Railroad,
recently stated that there are nearly 100,000 stockholders in the
Pennsylvania Railroad and its affiliated companies, and that the
number of its bondholders probably exceeded 200,000. Therefore,
if there are 1,250,000 stockholders of the railways and industrial
corporations, there are doubtless considerably more than 2,000,000
bondholders. Though there are many duplications in these figures,
the fact remains that the prosperity of probably 3,000,000 investors
is largely dependent upon the success of these corporations.
CORPORATION FINANCIAL REPORTS 309
While the number of stockholders has been increasing, the average
holdings of each stockholder have been steadily decreasing, and now
average ninety -eight shares. The stocks of the United States Steel
Corporation are great favorites among small investors. Taking the
stockholders' list, it was found that among one hundred people, chosen
at random, only nine own one hundred shares, or over, of both preferred
and common stock, while forty-seven have less than ten shares each.-
It is highly desirable that corporations should not only keep their
old stockholders, but should attract new ones. The surest way to
accomplish this end is to treat stockholders with the utmost frankness.
Although considerable publicity is already given to the affairs of the
larger corporations, further publicity is desirable. The average stock-
holder does not as a rule understand a balance sheet, and has only the
vaguest idea of his company's affairs. So long as dividend payments
are maintained, he is content. To be sure, a stockholder can always
get an impartial and valuable opinion from an investment banker con-
cerning the past records and future prospects of any company, but it
would be well if the annual reports of boards of directors to stock-
holders contained material from which the investor could judge for
himself to a greater extent. The material included should show the
records of the company over a period of years, for the company's
achievement in any one year may be unnecessarily discouraging, or
fictitiously encouraging. These records are most easily understood
when put in graphic form. With such graphic presentations any
stockholder can learn instantly how the fiscal year under review
compares with the several years preceding.
The American Telephone and Telegraph Company have for several
years shown on the back cover of their annual report a chart like Fig.
249 portraying the growth in their business. Fig. 2 also appeared
in an annual report of the same corporation to give a clear conception
of what becomes of the company's revenue.
Though Fig. 1 has not been used in any annual report, it shows a
type of chart which could very readily be included in a financial report
to give complete facts to stockholders regarding complex conditions
on which the average stockholder would gather very little information
from the kind of corporation financial report ordinarily sent to him.
The railroads have used charts in their annual reports to a greater
extent than the industrial corporations. Some of the railroad charts,
however, are not put up in such form as to be easily understood and,
310
GRAPHIC METHODS
with many of the charts, there is danger of misinterpretation. For
instance, it is not at all easy to analyze Fig. 220 so that its four dif-
ferent subjects may be compared.
Fig. 220. Percentage Increase in Freight Service on the
Illinois Central Railroad Since 1902. This Illustra-
tion Was Taken from the 1912 Annual Report of the
Company
Four distinct subjects are treated in this chart, but the horizontal bars
are arranged in such manner that the reader is likely to think there
is only one subject. Probably most readers would prefer to turn
the chart so that it may be read from the left-hand edge as four
separate curves. To a trained reader this information would be much
more clear if put in the form of curves like those seen in Figs. 224,
225, 226, 227
Fig. 221 also shows several different subjects which should be
compared, but for which comparison is not very feasible on the chart
as given. In Fig. 220 the four different subjects were so widely sep-
arated that comparisons were almost impossible, while in Fig. 221 the
four different subjects have the bars so arranged that it is difficult
for the eye to follow any one subject through the maze of bars.
In Fig. 222 the method of presentation is somewhat similar to
that used in Fig. 221. As seen in Fig. 222, however, the bars are
CORPORATION FINANCIAL REPORTS
311
II
111
III
arranged horizontally with the earlier year at the bottom, while in
Fig. 221 the bars are arranged vertically with the earlier year at the
right. In both of these charts the arrangement for successive years
is incorrect, for the charts give the impression that all quantities por-
trayed are becoming less in-
stead of greater as years go on.
The indiscriminate mixture of
so many different kinds of
bars in one chart makes a
complex diagram to interpret,
and it is probable that the
chart would at least be no
more difficult to apprehend if
made entirely in the form of
curves instead of bars.
Though it is true that curves
are not understood by some
people who can readily grasp
the bar method of presenta-
tion, there is no use in keeping
to the bar method if the bar
presentation is made as com-
plex as a chart involving
curves.
Fig. 223 was not printed in
a corporation annual report,
but it is included here because
it may show some possibility
for the inclusion of curves
in financial reports to give the
stockholder more complete
information than he would
otherwise receive. The data
of Fig. 223 are of interest
when considered along with
in minimi
I I ' Ml1 III!
„.
i n
i v m
Fig. 221. Freight Service and Traffic on the
Union Pacific Railroad and Auxiliary Com-
panies
This chart shows by years the per cent of increase over the
year ended June 30, 1898, in the gross revenue from the
transportation of commercial freight, the number of
tons of commercial freight carried one mile, and the
number of miles run by cars and locomotives in freight-
train service. Locomotive miles include revenue
freight-train miles, all mixed-train miles, and helping-
train miles
The illustration is reduced from the 1912 annual report
to stockholders. The backward arrangement of
years from right to left causes the first impression that
all quantities are growing less instead of greater.
Four subjects shown combined in one chart in this
manner are confusing. Either four distinct groups of
bars or four curves would be superior to the method
used here
the charts seen in Fig. 224, Fig. 225, Fig. 226, and Fig. 227. Fig.
223 is, however, misleading because the vertical scale does not extend
to zero and the chart gives the impression of a much larger per-
centage difference between net earnings and dividends than really
312
GRAPHIC METHODS
existed. Omitting the bottom of the chart makes the dividends
appear a smaller percentage of net earnings than they really were.
Fig. 223 could have been considerably improved, also, if the line
showing net earnings were made much heavier than it is seen in the
illustration.
Union Pacific Railroad
Fig. 222. Passenger Service and Traffic on the Union
Pacific Railroad and Auxiliary Companies
This chart shows by years the per cent of increase over the year ended
June 30, 1898, in the gross revenue from the transportation of passen-
gers, the number of passengers carried one mile, and the number of
miles run by cars and locomotives in passenger-train service. Loco-
motive miles include revenue passenger-train miles, all mixed-train
miles and helping passenger-tram miles, but do not include miles run
by motor cars
Here the reversed arrangement with the latest year at the top gives the
erroneous impression that passenger business is decreasing. A chart
like this does not assist greatly in conveying information to the stock-
holder
What figures for an annual report should always be shown in
chart form to make comparisons most clear is hard to determine,
but it will doubtless be agreed that, if possible, the charts should
CORPORATION FINANCIAL REPORTS
313
New York Times Annalist
Fig. 223. Net Earnings and Dividends of the United States Steel Corporation
The figures for net earnings are plotted by quarters. Dividend figures are plotted to show the total divi-
dends each year. The line at the top of the shaded area shows the dividend paid. Dividends exceed
net earnings in portions of the years 1911 and 1912, but the total earnings of those years were nevertheless
great enough to justify maintaining the dividend rate
Though this illustration contains some interesting information, the chart is misleading because the scale
does not extend to zero. At first glance, the dividend of 1909 would seem to be more than four times
the dividend of 1908 when in reality it is only about twice as large
attempt an answer to these questions that naturally arise in the stock-
holder's mind:
1. Has the earning power of the company been maintained?
2. Is the property being kept in proper physical condition?
3. Is the financial condition sound?
For the purpose of illustrating the advantages of the graphic
method for annual reports, the United States Steel Corporation has
been selected. The chart shown in Fig. 224 is designed to answer the
first question: "Has the earning power of the company been main-
tained?" In order to bring out more clearly the very important
relation between the surplus for dividends and the dividends paid,
curves Nos. 3 and 4 are redrawn on a considerably enlarged scale
as seen in Fig. 225. Curves No. 3 and No. 5 are therefore identical,
as are also curves No. 4 and No. 6.
Fig. 224 and Fig. 225 show that the Steel Corporation, like a
large number of railways and industrial companies, reached the zenith
314
GRAPHIC METHODS
DOLLARS
1,000, 000, 000
9OO, OOO, OOO
8OO, OOO, OOO
7OO, OOO, OOO
6OO, OOO, OOO
5OO, OOO, OOO
4OO, OOO, OOO
3OO, OOO, OOO
2OO, OOO, OOO
10O, OOO, OOO
'02 '03 '04 '05 '06 'O7 'O8 'O9 '1O 'II '12
Fig. 224. The Earning Power of the United States Steel Corporation
Curve 1. Gross earnings
Curve 2. Operating expenses
Curve 3. Surplus earned available for dividends
Curve 4. Preferred and common dividends paid
This chart and the following charts relating to the United States Steel Corporation are submitted as a sug-
gestion to show how the annual report of a corporation could easily give comparisons over several years.
The space required for the charts is insignificant, yet the stockholders would receive the vital facts in
such form as to permit a full understanding of the condition of their company as compared with previous
years
of its earning power in the year 1907. In that year more than 15
per cent was earned on the common stock, while only 2 per cent was
paid. Curve No. 1 shows that the gross earnings in 1907 were $757,-
000,000. Then follows, in 1908, the terrific slump in business due to
the financial panic, with a gradual but uncertain recovery. By 1912,
the corporation succeeded in bringing its gross business up to $745,-
000,000, still somewhat under the 1907 high-water mark.
The movement of operating expenses is depicted by curve No. 2.
A glance at the chart shows that, during 1905-6-7, gross earnings
tended to increase faster than operating expenses, which is again true
in 1909 and 1910. In 1908 and 1911, it proved impossible to reduce
operating expenses to conform to the reduction in gross earnings,
with the result that profits were sharply reduced in both these years.
In 1912, a unique situation occurs. Curves 1 and 2 run practically
parallel, showing that although the gross earnings were largely in-
creased, operating expenses kept pace. The largest factor in op-
erating expenses is naturally labor, and the reports of the corporation
CORPORATION FINANCIAL REPORTS
315
DOLLARS
ZOO, OOO, OOO
ISO, OOO, 000
I6O, OOO, OOO
140, 000, 000
12O, OOO, OOO
100, 000, 000
8O, OOO, OOO
6O, OOO, OOO
*4O, 000, 000
2O, OOO, OOO
'O2 '03 'O4 '05 'O6 'O7 'O8 'O9 '1O '11
Fig. 225. The Surplus Earned and the Dividends Paid by the United States
Steel Corporation
Curve 5. Surplus earned available for dividends
Curve 6. Preferred and common dividends paid
These curves are the same as Curve 3 and Curve 4, respectively. The data are depicted here on a large
scale so that the relation of dividends to surplus earned may be seen clearly
throw the necessary light on this item. The average wages per man
in 1907 were $765 per annum, and in 1912, $857. It has been shown
that gross earnings in 1912 were less by $12,000,000 than in 1907,
yet operating expenses in 1912 were $45,000,000 more than in 1907,
being, as the curve shows, over $600,000,000 for the first time in the
Corporation's history.
Curves 3 and 5, representing the surplus for dividends, are of most
interest to the stockholder. It will be recalled that when the Steel
Corporation was organized in 1901, the common stock was imme-
diately placed on a 4 per cent basis. In 1903 the disbursements to
the common stock ceased altogether and even the 7 per cent upon
preferred was seriously questioned. During 1906, 1907, and 1908,
2 per cent was paid on the common, and then in 1909, the rate was
first raised to 3 per cent, later to 4 per cent, and finally to 5 per cent.
Conservative people have always criticised the 5 per cent dividend,
believing that a 4 per cent rate would be more likely to be permanent.
However, a consideration of the relation of curve No. 5 with No. 6
will show that the Corporation has avoided the payment of unearned
dividends throughout its career. The margin was very slim in 1903
316 GRAPHIC METHODS
and 1904 and again in 1911 and 1912. As the balance of earnings
for the common stock in 1911 was only 5.9 per cent and in 1912 only
5.7 per cent, a continuance for another year of such narrow margin
would probably have meant the reduction of the 5 per cent rate,
especially in view of the reduced appropriations for new construction
and betterments, as disclosed in Fig. 226, Fortunately, however,
for the stockholders, conditions in 1913 improved enormously and
11.17 per cent was earned for the common stock. Considering only
the figures charted here, it is evident that the earning power of the
Corporation during 1912 was not maintained.
To answer the question "Is the property being kept in proper
physical condition?" the chart shown by Fig. 226 has been constructed.
As seen from curve 7, depreciation and repairs have shown a fairly
constant increase, the amount in both 1910 and 1912 exceeding that
of 1907, although the gross earnings were larger in 1907 than in either
1910 or 1912. This is a satisfactory sign.
Curve 8 portrays the total amount of money invested in the con-
struction of new plants, mills, etc. This curve reaches its height
in 1907 (running up to $67,000,000) and represents in large part the
creation of the great plant at Gary. Curve 8 shows that even the
panic of 1907 failed to curtail new construction to any great extent.
But the poor profits in 1912, coupled with the higher rate of dividend
on the common stock, did produce a sharp contraction — from $50,-
000,000 in 1911 to less than $15,000,000 in 1912— the latter figure
being the smallest since 1902. This, however, is not to be criticised
too severely, since it is clear that a continuous expansion in pro-
ductive capacity might easily outrun the normal consumptive demand.
Curve 9 represents the extent to which surplus earnings have
been "ploughed back" into the property. This tells how the water
has been squeezed out of the common stock. The report of the Bureau
of Corporations in 1912 shows that, whereas there was a capitalization
over indicated investment amounting to $625,353,559 in 1902, such
excess was only $281,051,222 in 1910. Furthermore the report expressly
states that this excess is not necessarily, nor entirely, "water". Up
to 1908, curve 9 follows curve 8 very closely, indicating that the new
construction was largely paid out of earnings, and not capitalized.
Since 1907, there has been a tendency to finance such additions by
the sale of bonds. This tendency, if not carried too far, is not open
to criticism. One may, therefore, answer the second question in the
CORPORATION FINANCIAL REPORTS
317
DOLLARS
10O. 000. 000
5O, OOO, OOO
4O, OOO, OOO
3O, OOO, OOO
2O, OOO, 000
1O, OOO, OOO
'O2 'O3 'O4 'O5 'O6 'O7 'O8 'O9 '1O '11 '12
Fig. 226. The Maintenance of Property by the United States Steel Corporation
Curve 7. Depreciation, repairs, etc.
Curve 8. Expenditure for new construction
Curve 9. Appropriation from surplus earnings for construction and betterments
No more lines or figures are placed on this chart than are really necessary. The intention was to make the
chart just as simple and clear as possible. Note the large quantities expressed by the numbers in the
vertical scale, yet the wide spacing of the groups of three figures makes interpretation very easy
318
DOLLARS
4OO, OOO, OOO
38O, OOO, OOO
360, OOO, OOO
34O, OOO, OOO
32O, OOO, OOO
3OO, OOO, OOO
28O, OOO, OOO
26O, OOO, OOO
24O, OOO, OOO
22O, 000, OOO
2OO, OOO, OOO
18O, OOO, OOO
16O, OOO, OOO
14O, OOO, OOO
120, OOO, OOO
1OO, OOO, OOO
SO, OOO, OOO
6O, OOO, OOO
4O, OOO, OOO
20, 000, 000
o
GRAPHIC METHODS
/
^^»
/
iQ^.
/
\
/
/
\
/
->
f-
X
r
1 —
<•"-
>•••
-— .
\\^
i?
^
•- —
**
•-^
^
^
'02 '03 '04 '05 '06 'O7 'O8 'O9 '1O '11 '\Z
Fig. 227. Financial Condition of the United States Steel Corporation in Different
Years as Shown by the Balance Sheet
Curve 10. Current assets
Curve 11. Cash holdings
Curve 12. Current liabilities
Here the numbers in the vertical scale represent larger quantities than in Fig. 226 and the spacing is closer
in the vertical direction. Nevertheless, the numbers are easily read. To avoid any chance of error
in interpretation it seems well to write out in full even the large numbers necessary here
affirmative, for from the evidence given, the property has been ade-
quately maintained.
Fig. 227 illustrates the financial condition of the company as dis-
closed by the balance sheet. This chart is very conclusive, for it
shows a very large excess of current assets over current liabilities,
while cash holdings have tended to equal or exceed the total cur-
rent liabilities. The balance sheet, therefore, indicates continuous
and increasing financial strength. Current assets in 1912 reach nearly
CORPORATION FINANCIAL REPORTS 319
$300,000,000, compared with $275,000,000 in 1907. Current liabilities
were $60,000,000 in 1912 and $45,000,000 in 1907, but cash increased
from $54,000,000 to $67,000,000. The Steel stockholder has, therefore,
good evidence that his company is being managed with great sagacity
in all departments.
An exhaustive study of the United States Steel Corporation would
require a great many charts similar to the foregoing, but those given
probably bring out clearly the main results in each annual report.
The use of graphics to drive home statistics is yet in its infancy, and
the next few years will doubtless witness a rapidly growing employ-
ment. There seems no good reason why any management, desiring
to tell the whole truth to its stockholders, should not adopt graphic
methods to supplement, as well as to illuminate, the statistical tables.
The famous economist, Stanley Jevons, wrote in 1875:
There is much to be learnt about money before entering upon those abstruse
questions, which barely admit of decided answers. In studying a language, we begin
with the grammar before we try to read or write. In mathematics, we practice our-
selves in simple arithmetic before we proceed to the subtleties of algebra and the
differential calculus. But it is the grave misfortune of the moral and political sciences,
as well shown by Mr. Herbert Spencer in his "Study of Sociology," that they are
continually discussed by those who have never labored at the elementary grammar
or simple arithmetic of the subject.
To-day, everyone still believes himself competent to discuss cor-
poration finance, which is a branch of political science, in the same
cheerful ignorance of the fundamentals of the subject. Everything,
therefore, which will help to throw light on the dark corners of finance
and make ignorance less excusable should be welcome. Never have
corporation managers been more sensitive to public opinion, and if
charts in annual- reports make the truth more easily grasped (which
they do) they will soon command an established place in corporation
records.
This chapter is largely based on an article prepared at the suggestion of the author by
Mr. Pierpont V. Davis, of New York City, and published by Mr. Davis in Moody 's
Magazine,
320
GRAPHIC METHODS
1263
s-ieio
a
8 te <! a
W P 0 t>
a
o o
^ »5 O
r-l(D !*•-< i-"CM CJ1O
*
o •* e» ea
41 n co
r- oo a X
K
O *4 Ct C9
^ w co
N oo o> X
,«
o -* c* »
•f » CO
a
o«
O <H C« «
^P <L>
t- 00 u) <->™
1 €
o -> « w
•jt n o
g
£ 5 Z £
cW o «
w ^ o
•8 o
O '2 d «d fe
» ft o 0 o
g
PW P. o o
fc fe r1 P
CO N O
pop
p OO ffl p CS 03
C3
• -<
O ^ !"o 3
iJ o !B W
0 0
M W fe
n o
~ C S
0 > N
W CQ W W
(3
^•g ^ |
S a •*
O L4 T3 ctj
O C CD P
O
'._• 0
0 J ' 0 3
W M (lj ij
.1 Q ( p5 y5
* %
a fi M
1 s I s
e
•
•
£3^^ & «^ O
a u
o e t,
R W to
o
ID fci f'-f
O Q ^ "" •" M
O O ? t^ *^J C
t
<JO * ^^ . t
HP H 3 fc> S
•w » , •£ .
e o « 3 S :- . fe -^
^ >
fJU
oM ^g ci» «<
£; PH fep4 fert feo
- ° "s9 °"° *">;
«S -Cs S-3 -J
<<j <<; «jta off
&o gS ^a
M CQ K CO ^ CO
^ o <tf o 5
33 SM ^4
i 0 . w § X 2
I O O 0 Q P 0
feta feca OH OH
% § o « .S 2 .2 S
-a - s to
OS -0 oS3 ^.5
P •> P^Q OH M&
o el
43 u
sfi
J5 h M S
*i P 5
o «< ez co
*
O « O rt
• B V 9
O
O «H « -1
O iO O
> t» 03
rt O -<
rt N C»
o o £ «
» Q O D
10 O^P 0 O
M w r* «?
IO
«*
g S S*5
S^^ fa i^
(« « -0 a
a
H
»•»
oo t» n o
4
« O C3 «
•<r oo co
CJ t» Ct
is „ .[
c* co t» oo
CD 5» CD N
13 -I H) •-!
r-
0
»< 10 « <!
0 0
'*•. , o
!J
S£>
W
3
0) «
5 3
03 0
W
C 4)
S
S
S M
I*
O
^3 §
o
S-5
M
g C8
o>
8*8
M
S 8
0)
a
&s
S «
03 ^
a a
I
S3
^•s
o
-1
§ g
2 S
•8
•2a
C o
H
§5
> CO
h
C 5?
•2 g
1*8
«l
cu *£
Is
ti-A
ST<
O--;
bfl o o>
Si M W
.3 ^
o >>«
rn i P
S o
P.
oo
-g§§
CHAPTER XVI
GENERAL METHODS
THERE are a number of comparatively little known short cuts
and convenient methods available in the collection and record-
ing of statistical facts. If obsolete or unsuitable methods are
used it may make a difference between success and failure in the work
of keeping records of any complex business. When the methods of
tabulation are too laborious, not only are the records so extensive as
to be in disfavor, but they may occasionally include errors, in spite of
the greatest care that can be taken by even the highest grade of employ-
ees. Anything which will reduce the amount of mental concentration
necessary on the part of persons collecting and tabulating facts, will
ordinarily assist in the production of more accurate final results. In
large statistical studies, such as are made by the United States Census
Office, it would be practically impossible to get all the information
now obtained if tabulating machinery were not brought to the aid of
the human brain and hand.
The punched-card system now widely used in" statistical work has
made possible an almost unlimited amount of subdivision of analysis
with very little extra expense. Fig. 228 shows the card used by the
United States Census Office for the 1910 census. One of these cards
was punched for each inhabitant in the United States in accordance
with the data obtained by the Census enumerators. It will be noticed
that the card contains different columns of names or numbers and that
there are twelve classifications possible in each vertical column in which
a punched hole may be made. Ordinarily the different columns are
used for different subjects, and the position of the punched hole in each
column records the classification of the data relating to that particular
subject.
The punched cards are stacked so that all are right-side up. It will
be noticed from Fig. 228 that the Iow7er right-hand corner of the card
321
322
GRAPHIC METHODS
is clipped off. If any card in the stack is arranged improperly, it will
show because the card will project beyond the other cards at the clipped
corner of the pile. The stacks of cards are run through a sorting ma-
chine such as is seen in Fig. 229. Needles connected to electric wires
make a contact through the
holes in the card, and operate
the sorting mechanism auto-
matically in such manner that
the cards are dropped into com-
partments in accordance with
the position of the punched hole
on the card. Cards are sorted
for one particular characteristic
at a time, so that all cards
having that characteristic are
obtained for tabulating pur-
poses. After the data on one
set of cards have been tabulated,
the cards can then be run
through the sorting machine
again and sorted for other char-
acteristics. This permits using
the punched cards over and
over again until all of the differ-
ent data which may be of
interest have been taken from
the cards by the tabulating
machines.
Fig. 230 shoWS the tabu- Courtesy of me Tabulating Machine Company
Fig. 229. Hollerith Card-Sorting Machine
Suitable for Use by Corporations for
Statistical Work Relating to Sales,
Costs, Etc.
This machine will sort about 12,000 cards per hour,
and place in the right compartment all cards having
the hole punched in the same position in the particu-
lar column for which the sorting is done
lating machine as used in the
general commercial work
of corporations, and for
State or municipal departments.
The cards are placed in the ma-
chine at the left and are fed
through automatically, one by one, so that electric contacts are made
wherever there are holes punched in the card. The electric contacts
cause the counting dials to revolve by just the right amount to record
properly the data for each punched hole.
GENERAL METHODS
After any group of cards has been run through the machine the
totals can be read off from the counting dials and written down by
the operator. Then the machine is ready for some other set of cards.
Machines are built with different numbers of counting heads to suit
the complexity of the data in any kind of business. By having several
counting heads on the same machine, different sets of information may
be taken from the cards simultaneously, thus frequently permitting
one run of the cards through a tabulating machine to give all the data
which may be re-
quired.
The punched-
card machines are
proving to be of
very great useful-
ness in commercial
work. Fig. 231 gives
a view of a com-
pletely equipped
office for the use
of the punched-card
system by an elec-
tric lighting com-
pany. The data are
transferred from the
original records to
the cards by very
simple punching
machines with keys
somewhat similar
to typewriter keys. The punching is usually done by girls. A little
training and practice gives high speed. Once punched, the cards are
always available and may be filed for record purposes. It is frequently
a great convenience to be able to run through the machines cards for
several years back so that comparative statistics may be made. The
preservation of the cards makes it unnecessary to dig out the original
records. The uniform size of the cards makes it possible to preserve
large quantities of them with comparatively little labor.
In punching the cards there are certain holes relating to depart-
ments, dates, etc., which are repeated time after time for large numbers
^joaitesy of the Tabulating Machine Company
Fig. 230. Hollerith Tabulating Machine for Totalling
the Data Contained on Punched Cards
The machine illustrated has four counters, permitting the simulta-
neous taking off of the data contained under four different headings
on the punched card. The sorted cards are placed at the left
of the tabulating machine and run through at the rate of about
3,000 per hour. Totals are read from the dials shown at the right
324 GRAPHIC METHODS
of cards. Instead of the operators punching these repeated holes one
by one in each card, the cards are punched by a gang punch, which at a
single stroke punches several holes in many different cards. The gang
punch can be seen in Fig. 231 on a table near the right-hand side of the
illustration.
Manufacturing companies now use the tabulating machines for
keeping track of the cost of different orders and of different classes
of work in the factory. The data from the original time slips of the
workmen are transferred by the punching machines to the cards day
by day as the time slips are turned in. The punched cards can then be
sorted by order number and department, so that when each order
is completed the total cost of all work on that order is obtained. The
distribution of the value of work done by different departments can be
had also if desired.
In keeping the records of a sales department, the facts relating
to the various sales orders are transferred to the punched cards and the
cards sorted and tabulated in any manner desired. A very large manu-
facturing business having many kinds of machinery as a product, uses
the punched-card system for each order as it is received in the plant.
At the end of each month the records show the total sales of each branch
house, the total sales of each salesman, the total sales .of each main class
of product, and many other kinds of information. In this particular
plant tabulating machines are of very great assistance, because they
can be used to make a sales analysis for any one class of product. The
punched card for each order shows the catalogue number of the product
called for by that order. Whenever desired, cards for a definite length
of time can be run through the machines so as to sort out all the cards
for any catalogue number of product on which a study is to be made.
The resorting of these cards by sales districts shows the distribution
of the total sales of this particular product by distinct districts, or
States, and, if desired, by different salesmen. The sales for the various
months or seasons of the year may be had if wanted. Though the data
relating to the many kinds of product need not be regularly tabulated,
the facts are nevertheless preserved so that tabulation for any particular
class of goods or any territory can be made whenever a study seems
desirable.
The multitudinous uses to which these card-sorting and tabulating
machines can be put are far beyond any possibility of naming here.
The very great flexibility, speed, and accuracy of the machines make
GENERAL METHODS
325
Courtesy of the Tabulating Machine Company
Fig. 231. A Completely Equipped Office for Collecting and Tabulating the Operating
and Sales Statistics of an Electric-Lighting Company
The girls at the left are operating the key punches for punching the cards. A gang punch is shown on
the table at the extreme right. In the corner is the card-sorting machine, and the tabulating machine
is in the center. Files for punched cards are seen along the wall
them almost indispensable in any work where there is large quantity
of complex data to be analyzed. It has been found feasible and profit-
able to use machines of this type in businesses of only moderate size.
The adding machine is now so commonly used that it seems scarcely
worth while to mention it here. There are, however, frequently times
when special investigations must be made, but adding machines do
not happen to be available, and the investigator feels seriously handi-
capped because he must take from the original records only those
items which may be of especial interest to him. In work of this kind,
it is sometimes convenient to use one of the small-size pocket adding
machines of which there are several different makes now on the mar-
ket. Though these machines are not at all in the same class as the
large key-operated machines, they are of assistance in taking off
occasional items because they overcome the necessity for putting
326
GRAPHIC METHODS
down the items on a piece of paper for addition later by mental effort.
With the portable adding machine the data are taken from the original
work directly and added automatically as the work proceeds.
Engineers do the greater portion of all of their computing work
by means of the slide rule. By others than engineers, however, the
slide rule is very little used. In the preparation of data for curves
and charts for corporation work, or for any investigations where
numerous percentages are necessary, the slide rule is almost indispen-
sable. A 10-inch slide rule as shown in Fig. 232 is sufficiently accurate
for most work, and, as it costs only a few dollars, it should be a part
of the equipment of everyone who is doing even the simplest form of
statistical work, or who is periodically plotting curves involving
ratios or percentages. By using a slide rule the percentage ratios of
numbers can be determined almost instantly and with no mental
effort. It can be confidently predicted that anyone who has much
multiplication or division to do in relation to curve-plotting and chart-
making will find the slide rule of such a great assistance that the
rule would not be parted with under any circumstances if a new one
could not be obtained.
Fig. 232. A 10-inch Slide Rule
The slide rule is of great convenience in doing work involving multiplication or division-
It is especially valuable for obtaining ratios or percentages in statistics for industrial
work
Judgment must be used in the showing of figures in any chart
or numerical presentation, so that the figures may not give an ap-
pearance of greater accuracy than their method of collection would
warrant. Too many otherwise excellent reports contain figures which
give the impression of great accuracy when in reality the figures may
be only the crudest approximations. Except in financial statements,
it is a safe rule to use ciphers whenever possible at the right of all
numbers of great size. The use of the ciphers greatly simplifies the
grasping of the figures by the reader, and, at the same time, it helps
to avoid the impression of an accuracy which is not warranted by
the methods of collecting the data.
A recent government report* contained this statement: "The
cotton crop of last year (1911) aggregated 16,250,276 500-pound
* " The Packing and Marketing of Cotton," by John M. Carson.
GENERAL METHODS 327
bales, the total value of which is $1,000,000,000 and, including the seed,
$1,200,000,000." The figure for the number of bales implies that
every single bale of cotton raised in the United States was accounted
for and that these figures are absolutely accurate down to one bale of
cotton. This denotes an accuracy of 1 part in 16,000,000 parts, or an
accuracy within 0.000006 per cent. It is very doubtful indeed whether
the figures for the cotton crop are accurate within 1,000 or even 10,000
bales. Suppose a possible error of 10,000 bales were assumed, and the
cotton crop put down as 16,250,000 bales, the accuracy would still
be 1 in 1,625, or within 0.06 per cent. For most purposes it would
be much preferable to use the round number 16,250,000 instead of the
detailed figures which were given in the Government report. The
particular report from which the figures are taken is not a tabulation,
but a written report in regard to the methods used for packing cotton.
Since the report was intended to be read by merchants and planters,
rather than by statisticians, it is all the more important that the
figures should be presented in round numbers so that they may be
easily grasped. The mere fact that values for the cotton in the latter
part of the quotation given above are in very rough estimates of such
round numbers as "$1,000,000,000", calls special attention to the
use of detailed figures for the "16,250,276 bales".
Misleading figures implying a greater accuracy than justifiable
are very often found as a result of the addition of different quantities
some of which are large and some small. The small quantities may
have a great degree of accuracy, but this does not give accuracy to
the sum of all the quantities, for the total cannot be any more accu-
rate than the most inaccurate item included in the total. If a very
large item is not accurate within ten thousand, then it is useless to
include in the grand total the three right-hand digits which may be
obtained as the result of addition. When some of the items included
are so small that they are in tens or hundreds, the addition should be
made to include all the digits. After the sum is known then all those
digits whose accuracy is doubtful in the total should be replaced by
ciphers.
Fictitious accuracy is quite often implied in the results of com-
putations where a slide rule has been used. The ordinary 10-inch
slide rule can give an accuracy of only three significant figures, and,
on the right-hand portion of the scale, the third figure is often some-
what in doubt unless very great care is used in manipulating the
328 GRAPHIC METHODS
rule. This means that with the 10-inch slide rule the accuracy is
ordinarily no greater than 1 in 1,000, or one-tenth of one per cent.
Though two quantities each running into five figures may be multi-
plied on the slide rule, the product would not be accurate beyond three
significant figures, and ciphers must be put down to express the re-
mainder of the number for the product.
If very large quantities obtained by slide-rule computation are
added together with a number of small quantities, the total cannot,
of course, be accurate beyond the third or fourth digit toward the right
of the largest quantity included in the total. The fourth digit may be
fairly accurate in the total, because in the process of addition the
various figures added would tend to give a close approximation of the
fourth digit and that digit might accordingly be put down in the total
because it has at least a fair possibility of accuracy.
It must not be assumed from the preceding paragraph that the slide
rule gives figures too crude for ordinary use. There are comparatively
few sets of data relating to costs, output, or other records of industrial
work which have an accuracy greater than one-ten.th of one per cent.
For the great majority of ordinary problems, the data are so crude that
the 10-inch rule has more than sufficient accuracy. The use of the
slide rule on many classes of work has a desirable psychological effect,
in that it calls attention to the accuracy of the data and assists in pre-
venting unnecessary detail work which it is very easy to drift into if
any assumptions of great accuracy are permitted to creep in.
The question of significant figures in statistical work and even in
ordinary commercial reports is an important one which should have
greater attention than it ordinarily receives. Unfortunately the sub-
ject can be only briefly touched upon here and the reader would do well
to look the matter up in some of the books on statistical theory.*
It sometimes happens that a few blue prints are required from
some complex chart made on heavy paper or cardboard. Instead of
making a tracing from the drawing by means of tracing cloth and with
great expenditure of labor and time, it is sometimes feasible to treat
the original drawing with a transparentizing solution so that blue
prints can be obtained directly. The transparentizing solution is put on
the paper with a brush or sponge and then blue prints are made in the
ordinary manner. There are several different makes of the trans-
* A chapter on " Approximation and Accuracy " will be found in " The Elements of Statistical Method," by Willford I. King,
published by the Macmillan Company, New York City.
GENERAL METHODS 329
parentizing solution on the market and a supply can be obtained from
most shops selling drafting materials.
During the last few years very convenient photographic machines
have been put on the market which photograph directly on sensitized
paper without the use of any negative. With this type of machine,
copies of drawings can be made very cheaply and clearly. One of the
convenient features in doing work by this machine is that drawings
can be enlarged or reduced within a wide range of sizes. The machine
most commonly used for this work is called the photostat. In most
large cities there are companies equipped with the photostat appara-
tus who will at reasonable cost make copies of drawings sent to them,
much as the blue-printing companies make copies from tracings. Some
of the best equipped libraries have now installed photostat machines
as a convenience to their patrons. In a library so equipped it is pos-
sible to have a copy made from any page in any book or periodical in
the library. In the New York Public Library, the reader need only
fill out an order form giving the exact page and the name of the publica-
tion from which the copy is to be made, and state the size desired in the
reproduction. Usually the copy is available within a few hours, but,
if desired, it may be mailed, thus avoiding any necessity for waiting
on the part of the person ordering the copy. In case of rare books or
manuscripts, copies may be made page by page so that a complete copy
of the book is obtained without prohibitive expenditure.
Charts from which plates must be made for printing are nearly
always drawn considerably larger in size than the completed illustration.
Most of the charts in this book were drawn two or three times as large
as seen here. A photographic reduction in the size of the chart tends to
eliminate minor irregularities and gives a much better result than can
possibly be obtained from drawings in the exact finished size. In
making the original large-size drawings it is almost essential that a
reducing glass should be used to make certain that the finished drawing
will have the desired appearance. With complex drawings it is often
difficult to tell whether the lettering and figures are of large enough size
to be read easily after they are reduced to the size to be used for print-
ing. By looking through a reducing glass it can be determined at
once whether the drawing is in correct proportions. A reducing glass
is similar in appearance to the ordinary magnifying glass, but the lens
is ground concave instead of convex so that everything seen through
the glass appears of smaller size. The ordinary reducing glass can be
330 GRAPHIC METHODS
used for a reduction through quite a range of different sizes by holding
the glass at different distances from the drawing which is being con-
sidered.
One of the commonest errors made by the beginner in preparing
charts from which printing plates are to be made is that he does not
allow for the reduction in widths of the various lines. If the printing
plate is to be made one-third the lineal dimension of the original draw-
ing, it is essential that the lines on the original drawing should be made
three times as wide as they are to appear when printed. The novice
will find that even though he uses a reducing glass with great care, his
heavy lines will at first nearly always appear less wide and black than
he had expected and hoped that they would be.
Quite often it is desired to change the proportions of some chart
so that the ratio between height and width may be different from that
of the original drawing. Though the photographic process used in
the photostat machine or by the engraver (in making plates for print-
ing) permits a change in size, the same proportions remain between
width and height. There would seem to be enough demand to justify
an engraver making a combination of lenses by which one dimension
of a drawing may be changed more than the other dimension. By
using two lenses having cylindrical surfaces and having the axes at
right angles, there might be a possibility of changing the proportions
of drawings which are copied without any great amount of expense
after the apparatus has once been designed.
Very often persons owning cameras do not know that the camera
manufacturers are in many cases able to supply auxiliary lenses by
which pictures and copies of drawings may be made practically full-
size with ordinary cameras. Though the arrangement is not as con-
venient to use as a regular copying camera, it may be of great service
to supplement the work of a camera already owned.
It is not generally known that line plates may be made from charts
drawn on co-ordinate paper ruled with green ink. Such charts sent
to many zinc engravers are returned with the statement that it is
impossible to make a line cut from green-ink copy. The statement
is made in most cases by the engraver without even attempting to
make the cut. There is no difficulty in making excellent zinc cuts
from copy using the ordinary green ink, and many of the cuts in this
book have been so made, as, for instance, Fig. 156, Fig. 207, and
Fig. 215.
GENERAL METHODS 331
Of course, when line cuts are made from charts having a green-ink
background, the printed illustration shows both the black and green-
ink lines as black, and there is no distinction between the different
lines. On this account, it is necessary for the person ordering the
charts made from paper having green-ink lines to make certain that
the main features of the chart stand out with prominent broad lines,
so that there may certainly be a contrast in the width of the lines
when printed, to make up for the contrast obtained in the original
drawing by the difference in color of the two inks used.
Color printing is not yet ordinarily available unless a very large
number of copies are to be made. In order to make areas stand out
in contrast, different kinds of cross-hatching put on by hand ruling
have been used very commonly. One trouble with the hand ruling
is that it lacks uniformity unless done with very great care and to a
scale considerably larger than the finished illustration, so that there
may be enough photographic reduction to eliminate many of the de-
fects which would otherwise appear. It is not widely known that
there is a method available in the form of Ben Day mechanical shading,
which is far superior to cross-hatching for line-plate work. Most
good engravers can do Ben Day work, and it is just a matter of speci-
fying what kind of shading is desired on the different portions of the
drawing. With the Ben Day shading, more degrees of shading from
light to dark are feasible than with hand work, and, in addition, there
are many varieties of lines and patterns which may be used.
Since Ben Day work must be applied on each area separately by
means of a transfer process, it is necessary for the engraver to make
certain that the Ben Day shading shall not appear on some portion
of the zinc plate where it is not desired. This requires that the en-
graver must protect the different portions of the zinc plate by a paint-
like covering, and this must be done for each of the different kinds of
shading used. It is almost impossible to make any square-inch price
rate for Ben Day work because each new plate is a problem in itself.
The work is ordinarily charged for on a time basis, the usual rates
being from $1.00 to $1.50 per hour.
When copy to receive Ben Day work is sent to the engraver it
is marked somewhat as shown in Fig. 233, so that the instructions
to the engraver may be explicit. Crayon marks specify by number
the kind of Ben Day shading desired, and arrows point to the different
areas to be shaded. This marking of instruction is done with a blue
332
GRAPHIC METHODS
pencil because blue does not photograph easily and has such a small
effect on a photographic plate that it does not spoil the copy for making
a good zinc plate. In order to make the zinc plate from which Fig.
233 was actually printed, a red pencil was used for the bottom portion
of the illustration referring to Ben Day work. Red photographs as
black, and a zinc plate was obtained which shows the marking such
as would be used with a blue pencil when Ben Day work is ordered
from an engraver. Ben Day work has been used on a great many illus-
trations in this book, and it is believed that the reader will have no
difficulty in distinguishing the cuts with Ben Day work from those
cuts for which hand shading was used.
<° S
w «£
w ^t
O
00 ®
2 §
.6, d
oo-
«> g O
q q cu
d 6 d
r* ^.
8 t
10 <0
<0 CO
<o -t
O O O
r- w
cu 6
O O
fl
(0 «VI
-
C^
u>0
233. Copy from Which a Zinc Plate Is to Be Made with Ben Day Mechanical
Shading
This is the copy from which the plate for Fig. 1 was made. The areas to receive the Ben Day work are
designated by arrows and numbers naming the particular kind of shading desired. Sample books give
a wide choice of shadings. The markings on the face of the copy regarding the Ben Day work are made
with blue pencil, since blue does not photograph dark enough to affect the line engraving
GENERAL METHODS
333
There are a great many problems in graphic work which puzzle
the person getting up a chart if there are three different variables
to deal with. The problem, as ordinarily found, involves two differ-
ent independent variables, and a dependent variable depending upon
each of the two independent variables. Isometric drawings like Fig.
235, or solid models such
as are seen in Fig. 236 g| |[| \\\] |\|
and Fig. 237, can be
used, but they require a
great deal of labor and
care to make and are
accordingly not often
seen. There is another
method not perhaps so
obvious as a solid model
but nevertheless of great
value. When the data
follow any definite nat-
ural laws a chart on the
i p TV net A ' ft Courtesy of Data, Chicago
style of Fig. 234 is often Fig 2^ Chart for Obtaining the Weight of steel
simple to make and easy Plates ^-inch Thick and of Various Widths and
to interpret. By such Lengths
, A chart of this general type permits using three variables. The two
CiiartS many COmpUta- independent variables here are length and width. Weight is the
dependent variable. This kind of chart is much simpler to
construct than an isometric drawing like Fig. 167, or a model like
Fig. 236 or Fig. 237
UNSTHM //wa
tions may be made with
accuracy and ease.
In obtaining curves like those shown in Fig. 234 one of the variables
is made some constant quantity, and the other two variables are then
used to work out the data from which the curve is drawn. It can be
seen, for instance, that if a definite weight and length of steel plate
3/s inch thick is assumed, the width is absolutely fixed. To obtain a
curve like that seen for 5 pounds in Fig. 234, it is necessary only to
assume a weight of 5 pounds, then choose separate lengths one by one,
and compute the widths which would correspond with the lengths
selected to give a weight of 5 pounds. The various figures of width
obtained are then plotted as points for the 5-pound curve, and a smooth
curve is drawn through all of the points, giving the result seen in the
illustration. After one curve has been plotted another weight is
assumed in a similar manner, and new computations are made for
various lengths on the horizontal scale. Though this method of chart-
334
GRAPHIC METHODS
ing requires some little labor in making the various computations, it is
a very excellent one where the chart must be used for frequent reference.
The information from such a chart as seen in Fig. 234 may be read from
any portion of the chart, even though the intersection of the length and
width lines for the size of the plate under consideration does not fall on
one of the curve lines drawn. It can be seen for the example stated in
the lower left-hand corner of the chart that the intersection of the ver-
tical and horizontal lines of the independent variables falls halfway
between the curve for 20 pounds and the curve for 25 pounds.
The weight is accord-
ingly taken as 22}^
pounds.
Though the sub-
ject cannot be fully
gone into here, it may
be suggested for those
who care to consider
further the general
type of charts repre-
sented by Fig. 234,
that much work may
be saved by making
such charts on loga-
rithmic paper. This
subject has been dis-
cussed at greater length
in a preceding chapter.
Data of Guido H. Marx. Courtesy of the Standard Corporation, Philadelphia
Fig. 235. Relations Between Arc of Action in Inches,
Pitch Speed in Fee* per Minute, and Breaking
Load in Pounds, for Cut Cast-iron Gears of Ten
Diametral Pitch
This illustration is drawn on isometric ruling, with the ruling itself
seen only as a background so as to give the appearance of a solid
model in three dimensions
There are many classes
of data which, when
plotted on ordinary
squared co-ordinate
paper, involve plotting
many points to produce curves like those seen in Fig. 234, but
for which the same data shown on paper with logarithmic ruling
would give straight lines. When the curve lines are straight lines, it
is necessary to plot only two points for each curve and then draw a
line connecting those two points. This permits a very rapid construc-
tion of the chart. A little practice in the making of charts is necessary
before one can determine clearly the best method to use so as to produce
GENERAL METHODS
335
a simple chart. Paper having logarithmic ruling in both directions is
the kind most frequently used for mathematical charts. Such paper
can be purchased from almost any good store selling engineering sup-
plies. Readers wishing to go further into the preparation of charts of
this rather highly specialized character are referred to the excellent
work of Mr. John B. Peddle,
entitled "The Construction
of Graphical Charts", pub-
lished by the McGraw-Hill
Book Company of New York
City.
The use of isometric pa-
per for drawing charts repre-
senting three dimensions
was mentioned for Fig. 167.
In Fig. 235 we have another
application of this same iso-
metric ruling. Instead of
showing the whole sheet of
isometrically ruled paper as
a baCKgrOUnd, r Ig. ZOO SJlOWS Data of E. s_ parweU. Courtesy of the American Machinist
only enough of the iso- Fig. 236. Tests of a Direct-connected Fan and
metric ruling to give the im- J^F?16- T^M£del SJjJ8 the Effect on the
Efficiency of the Fan of Different Outlet Open-
pression ot three planes meet- ings and Of Different Speeds of Operation
ing llKC One Corner Ot a bOX. Curves are plotted on cardboard by assuming constant values
TViA nVmrt illnctratino- tViA for one of the three variables, and then plotting the rela-
Lustratmg tions for the other two variabjes Each of the curves is
data is drawn On the isomet- cu* ^rom tne cardboard and slit halfway up or down the
line for intersection with the cards at right angles to it.
TIC ruling SO that it appears Cards are fitted together to give the effect seen above
as though placed in a corner
made by the three planes. Parallel ruled lines then permit reading the
chart from any one of the three different scales. The dependent
variable is made the vertical scale here, just as in most charts where
there is only one independent variable instead of two. The use of the
isometric ruling is not as common as it would be if it were more widely
realized how easily charts may be prepared to give the effect of solid
models without the great labor which a solid model necessarily involves.
Fig. 236 shows another method which may be used instead of the
more laborious and costly solid model. Different curves are plotted
by assuming at frequent intervals constant values for one of the vari-
336 GRAPHIC METHODS
ables of the data, and then plotting curves for the other two variables.
These curves are made to the same scale on sheets of cardboard, and
then the outline of the curve is cut out with shears so as to give
a series of different cardboard curve sheets. The several sheets are
carefully marked for their intersecting points, and are then cut half-
way through in the upward and downward direction on the intersection
lines so that the curve sheets may be fitted together to give an effect
like that seen in Fig. 236. A cardboard exhibit on the scheme of Fig.
236 is, in many cases, just as satisfactory as a solid model and it has
the advantage of being quite easy to prepare without any special
apparatus or materials being required.
Fig. 237 shows a solid model of the type which may be considered
the acme of graphic work when there are two independent variables.
A model of this kind is ordinarily made of plaster of Paris, as that is a
material easily handled and capable of being made into any shape
desired. In making such a model the usual procedure would be to
rule a flat board with lines at properly spaced intervals for each of the
two horizontal scales. Computations made by methods similar to
those described for Fig. 236 would give the value, on the vertical scale,
for each set of conditions corresponding to the intersection of each two
lines ruled for the base and showing the horizontal scales. In Fig. 237
the cost computations can be considered to give points on curves drawn
on the surface of the solid model. These curves correspond exactly
with the curves drawn on cardboard in Fig. 236. In order to locate
the curve points which determine the surface of a solid model like Fig.
237, wires are driven into the bottom board at the intersection of the
ruled lines of the two horizontal scales, and these wires are made just
the proper length to represent the figures computed for the dependent
variable. When all the wires are in position on the board, a box is
made the right size for the base of the finished solid model, and with
sides as high as the solid model is to be made. This box serves as a mold
into which the wet plaster of Paris is poured. Care must be taken to
have the bottom edges of the box fit well on the board so that the liquid
plaster of Paris may not leak out.
The powdered plaster of Paris may be obtained from any store
selling building supplies, or from a drug store. Water is added and
the mixture carefully stirred until it is free from lumps and of about
the consistency of very thick cream. The fluid is poured into the
box up to the desired height and allowed to stand for several hours
GENERAL METHODS
337
or over night until it becomes thoroughly hard. The box is then
removed. In order to get the shape of the model as seen in Fig. 237,
the plaster of Paris is very carefully scraped away with a piece of
tin or some other simple tool until the ends of the vertical wires just
show through. Before the plaster of Paris is poured in, care should
be taken to mark the different sides of the board so that it will be
R. E. Scott, in Harvard Engineering Journal
237- Three-dimensional Model Showing Cost of Light in
Cents per 1,000 Candle-hours with 4O-watt "Mazda" Lamps
for Any Practicable Combination of Efficiency and Smashing
Point. Price of the Lamp is 50 Cents and Cost of Electric
Current is Assumed at 10 Cents per Kilowatt Hour
Three variables are considered here. The two independent variables are repre-
sented at the base of the model and the dependent variable, "cost", is read from
the vertical scale. A model of this kind can be made from plaster of Paris
by following the methods described in detail in this chapter
known in which portions of the plaster of Paris block the greatest
amount must be removed before the wires come in sight. Knowledge
of the position of the wires in the block of plaster of Paris permits
removing the plaster rapidly without danger of taking off too much.
After the wires do come into sight, the model must be carefully scraped
so that the surfaces will have uniform curves without any humps or
338 GRAPHIC METHODS
hollows. If all the surfaces are concave, as they are seen to be in
Fig. 237, the scraping is rather a simple matter since the surfaces
between the two wires are lower than the wires themselves. If a
solid model were made for data such as that of Fig. 236, much care
would be necessary, for in that case some of the surfaces are convex
and it would be essential that enough material should be left between
the different wires to permit giving the nicely rounded smooth surfaces
which would correctly represent the data. When the surfaces have
been scraped as nearly as possible to the proper shape they may be
smoothed by rubbing with fine sandpaper. The external flat faces
of the model may also be sandpapered advantageously to remove
any marks which may remain from the surface of the box used as a
mold. Lines such as are seen in Fig. 237 can be ruled on the surface
and the different scales can be lettered by hand. A few coats of boiled
linseed oil will harden the surface and give an attractive finish.
In Fig. 237 the lines giving oval figures represent certain oper-
ating conditions which, from experiment and from study of the model
itself, have been found to be most desirable in practice. The oval
lines show the limiting conditions best for actual practical operation,
and give the real conclusions which the model itself greatly assists
in portraying. Solid models and three-dimension charts like those
shown are of supreme value in studies of complex data. It is to be
regretted that these methods of presentation involve so much labor
that they cannot be used as frequently as might be desired.
In political campaigns frequent use is made of statistical informa-
tion. Campaign orators use figures which sound impressive when
combined with a certain amount of eloquence. Too many of the state-
ments, however, tell only a portion of the whole truth, and that por-
tion is, of course, assumed to be the portion which the speaker most
desires to have put forward. It is not ordinarily feasible in a speech
to give all the facts over a series of years so that the hearer may draw
any conclusions for himself. The whole system is weak in that the
audience are forced to depend too largely on the statements made
by the orator, rather than to draw conclusions of their own from data
which are warranted to be authentic. When we have a larger number
of people who know how to read curves, it will be a simple matter
to present the arguments of a political campaign by means of a pro-
jecting lantern with properly prepared charts thrown on a screen.
Even now the charts could probably be so made as to be understood
GENERAL METHODS 339
and correctly interpreted by the average person attending a political
meeting, with resultant increase in the effectiveness of the arguments
they support.
In municipal campaigns, especially, the lantern talk could be of
very great interest to the voters if the slides were carefully prepared
and arranged in a logical sequence. By using simple methods of
charting, almost any kind of facts could be portrayed so that they
would surely be correctly understood. Concise statements in con-
junction with the charts should, of course, be used, somewhat as the
main titles are placed under the illustrations of this book. Slides
showing snappy questions could be thrown on the screen rapidly,
and the succeeding slides could then answer the questions. Recent
public improvements, bridges, etc., could be illustrated by maps and
actual photographs. Pictures of fire apparatus and views showing
the efficiency of the street-cleaning methods, etc., could be used to
add interest and to bring out certain points in regard to the operation
of specific departments. There is no doubt that properly prepared
lantern slides would have great weight with the voters, for lantern
slides might seem to present a less biased point of view than would
the average partisan campaign orator.
In using lantern slides for campaign purposes it is not necessary
to have a large hall for each showing of the lantern slides. Auto-
mobiles could readily be equipped so that two cars could work to-
gether. One auto would carry a screen, which could be very quickly
put up, somewhat in the manner of a sail, when that part of the town
had been reached where the lantern talk was to be given to a crowd
in the street or on some vacant lot. The other automobile could carry
the lantern on a stand between the front and rear seats. The power
for the lantern would be obtained in the ordinary manner from tanks
of oxygen and hydrogen carried in the car. A car containing the lan-
tern equipment would be entirely self-contained and no electric wires
or other attachments would be necessary. The lantern car would be
stopped the proper distance away from the lantern screen on the
other car, and the slides could be shown on the screen within three
minutes after arrival in any desired section of the city. In thickly
populated districts it would probably not be necessary to announce
a political meeting of this kind, as word would be passed very rapidly
that a lantern talk was in progress and the desired crowd would collect
spontaneously.
340 GRAPHIC METHODS
One very great advantage of the lantern presentation in political
work comes from the fact that after one good set of slides has been
prepared, these slides may be duplicated at very small expense. Twen-
ty or even fifty sets of slides might be shown in different parts of a
city simultaneously on the last few nights just before election. The
main candidates are never able to make speeches at all of the desired
points during the last few days, and they probably always feel that the
last days or hours before an election are the most valuable of the whole
campaign. When many sets of lantern slides are made from the same
original charts there is very little additional expense, and the number
of people who may get the benefit of the carefully prepared slides is
tremendously increased. In every city there are many young lawyers
or business men who would be willing to make a speech to accompany
the slides if they could depend upon the slides for their main material.
The number of people who may be reached during the last few hours of
a campaign is thus almost unlimited if the lantern-slide method of pres-
entation is used.
From the educational point of view, it would probably be very de-
sirable to have lantern slides used in campaign work, because there
would be a very great amount of valuable information conveyed by
the slides shown. With lantern slides showing well prepared charts,
probably ten times as much information could be absorbed by an au-
dience as could be obtained by listening to the most expert campaign
speaker. In addition, there would be the great advantage that the
facts presented by lantern slides would be understood and remembered
months after the oratory of a campaign speaker had lost its beguiling
effect and his statements been forgotten.
It need not be thought that lantern talks such as are suggested need
be devoid of all those spectacular climaxes which are so common with a
campaign orator. Whenever it is desired to raise some enthusiasm, a
photograph of a candidate could be thrown on the screen and a cheer
would be sure to follow. There is an almost unlimited field for the
exercise of ingenuity in the preparing of campaign charts. The sets
of slides would have tremendous educational value, as well as great
power in presenting political arguments in such manner as would most
positively affect the vote.
Methods used by newspaper offices and political clubs for giving
out election returns to great crowds in the streets on the night of elec-
tion day are not all that they might be made if a little thought were
GENERAL METHODS 34)
given to the subject. Though the projecting lantern is now used almost
universally in presenting election returns in large cities, thus far the
lantern slides give only very brief scrawled statements that certain
cities or certain districts have gone for some particular candidate
with some estimated plurality. A person coming out into the street
after an evening at the theater has no way of knowing the import of
the various telegraphic statements which may have been thrown on
the screen earlier in the evening. It is only by watching the bulletin-
board screen for half an hour or more that a newcomer is able to get any
definite idea of how things are going.
When arrangements have already been made for using a lantern to
show the returns on a screen, it would cost comparatively little more
to give election returns which would be of much interest to the whole
gathering, as well as of great effectiveness in showing the situation
clearly to any newcomer who might join the crowd. For a national
election, slides could be prepared to the number of twenty-five or more,
giving an outline map of the United States and showing only the State
lines. As the returns come in, some man well acquainted with the
political situation could summarize the telegrams received up to the
last moment and give his opinion as to which candidates are leading
each State. A person accustomed to coloring lantern slides could then
immediately color in one of the map slides according to some key, so
the colors red, green, yellow, etc., on different areas would show that
certain candidates were ahead in those States or districts. For muni-
cipal elections, the wards and different divisions of the city could be
colored in exactly the same manner as suggested for the States. The
appearance of the suggested map as thrown on a screen may be judged
somewhat from, the map seen in Fig. 177. It would add much to the
enthusiasm of the crowd if it were announced before election day that
some well-known person would make the summary estimates from which
the colored slides would be prepared. It would probably take less than
fifteen minutes to color a lantern slide after the summary had been made
up by the person watching the telegrams, and it would be feasible to
show on the slide itself the hour at which the slide "went to press",
as 9.30 p.m., 9.45 p.m., etc. As a new slide could be prepared about
every fifteen minutes, a map summary shown on the screen need be
only about fifteen minutes behind the latest telegraphic reports.
In addition to the actual colored map, each slide should contain
colored bars which would show by their length the estimated summary
342 GRAPHIC METHODS
of all the States or districts, so that the totals of different candidates
might be easily compared. Thus, in a presidential election, the count-
ing of the number of States for each candidate does not by any means
give the whole story. The important thing is the number of electoral
votes, and these would be best represented by the bar summary which
would take into account the number of electoral votes of each State
estimated as won by any candidate. With the combination slide show-
ing, in the form of bars, both a map and estimated totals, any person
coming out of the theater to join the election-night crowd could see
instantly how the situation stood up to the moment the last slide was
colored.
With the election-return method outlined, the concise telegrams
in handwriting would still be shown on the screen one by one as the
news came in over the wire. A popular appeal to a large crowd can
always be made by snappy statements such as "Jones concedes Chicago
to Smith", or "California goes for Brown". Instead of holding state-
ments of this kind on the screen until other news could arrive, however,
any statement in written words would be taken off as soon as it had been
grasped by the crowd and one of the colored maps would be thrown on
the screen. Slides with colored maps and colored bars would be used
as fillers, to be kept on the screen continuously whenever there were
no telegraphic reports to be projected on the screen in written words.
It would probably be found desirable, in many cases, to show telegraphic
reports in such manner that a map would be thrown on the screen be-
tween each two telegraphic reports, and also held on the screen whenever
telegraphic reports should not come in fast enough.
Election returns are sometimes told to a whole city by search lights
thrown from the top of some high building. National, State, or munic-
ipal election returns can be kept distinct by the search-light method if
certain directions, north, east, south, or west are announced for the
lantern beams referring to the different kinds of election returns.
Until complete reports have been received the lantern beams can be
moved gradually up and down. After complete reports are in the beam
can be held steady, so that the watchers even miles away may know
from the angle of the light and its position that a conclusion has been
reached, and who wins.
Educational material shown in parades gives an effective way for
reaching vast numbers of people. Fig. 238 illustrates some of the floats
used in presenting statistical information in the municipal parade by
GENERAL METHODS
343
Photo bv the International News Service
Fig. 238. Statistical Exhibits in the Municipal Parade by the Employees of the City
of New York, May 17, 1913
Many very large charts, curves and other statistical displays were mounted on wagons in such manner that
interpretation was possible from either side of the street. The Health Department, in particular, made
excellent use of graphic methods, showing in most convincing manner how the death rate is being reduced
by modern methods of sanitation and nursing
the employees of the City of New York, May 17, 1913. The progress
made in recent years by practically every city department was shown by
comparative models, charts, or large printed statements which could
be read with ease from either side of the street. Even though the day
of the parade was rainy, great crowds lined the sidewalks. There can
be no doubt that many of the thousands who saw the parade came away
with the feeling that much is being accomplished to improve the condi-
tions of municipal management. A great amount of work was neces-
sary to prepare the exhibits, but the results gave ample reward.
CHAPTER XVII
A FEW CAUTIONS
THE title for any chart presenting data in the graphic form should
be so clear and so complete that the chart and its title could
be removed from the context and yet give all the information
necessary for a complete interpretation of the data. Charts which
present new or especially interesting facts are very frequently copied
by many magazines. A chart with its title should be considered a
unit, so that anyone wishing to make an abstract of the article in
which the chart appears could safely transfer the chart and its title for
use elsewhere. In the preparation of this book it has been found that
a number of the charts used have been copied from one magazine to
another, and that the titles under the charts have suffered much in the
copying. This is due chiefly to the fact that the titles are not considered
as an integral part of a chart, and that many magazine editors feel at
liberty to use for a chart whatever title they happen to see fit. If
each chart as first presented has a complete and clear title it will greatly
assist in establishing a practice that anyone making a copy of a chart
should copy the title as well as the chart itself.
It is unfortunate that so many authors send in illustrations or charts
for magazine articles without the titles to be used with the illustra-
tions when printed. This often forces the editor to make the titles,
and if he does not have complete information before him he cannot be
blamed if he makes a mistake by using a title which does not correctly
represent the data of the chart. To avoid the possibility of error,
the editor may use only the most brief title under the illustration, and
then trust to the chart being fully described in the context which goes
with it. In such a case, the reader who may happen to be especially
interested in the chart is forced to plow through a great quantity of
context to find the particular paragraph which may happen to explain
the chart. Though it is true that great care is necessary to give in a
344
A FEW CAUTIONS
345
few words a title for a complex chart, the result is well worth the effort
and a chart should not be considered complete until such a title has
been made.
When large numbers
of curves and charts are
used by a corporation,
it will be found advan-
tageous to have certain
standard abbreviations
and symbols on the face
of the chart so that in-
wife of
ttncr of
associ-
uduated
in 1884
(red In
he late
ay
sllgh u. ,i3 salt,
he contributed.,
or Mrs. Hayden, ho o:
re just where she was, •
r... jeder said that some ,
nfided to her that she had.thou
._ id seen Mrs. Hayden yesterday
noon In New Yori<.
KANSAS PROUD OF RECORD
&.
int
Has Reduced Drinking 2,000 Per
Cent. In 30 Years — Jails Are Empty.
Speciti to Tht New York Times.
TOPEKAk Sept. 18.— That Kansas has
reduced Its drinking 2,000 per cent. In
thirty years, and Its per capita consump-
tion of liquors Is how $1.48 as compared
with Missouri's $24 a yeai% Is the mes-
sage sent to Tennessee to-day by John
8. Dawson, Attorney General. Tennessee
ha's a prohibition fight on its hands this
Fall.
"The test of
value of prohibition
Bureau-
day des
aa Btrlc
aim up
downw
dlrectlj
Admij
present
nary
agair
Dr
Fig. 239.
A Clear and Accurate Title is of Great
Importance
The clipping above, taken from the front page of a very prom-
inent newspaper, shows an absurd title. If a thing is reduced
100 per cent, it is all gone. How can drinking be reduced
2,000 per cent?
formation may be given
in condensed form as a
signal to anyone reading
the charts. Fig. 240 is
shown here as an ex-
cellent example of what
may be done in mak-
ing symbols which would
be instantly understood
by anyone seeing them.
Though these particular
symbols are not fitted for use in chart drawing, they may give a sugges-
tion of the possibilities which exist for abbreviating into symbol form
certain remarks or instructions, which it may be frequently convenient
to place on the face of a chart as a guide to prevent misinterpretation
by the reader. If the symbols for chart work are not too numerous,
they would very soon be understood by each of the persons who
regularly go over the operating charts of a company.
It may be well to point out here that very large charts are sometimes
a disadvantage rather than an advantage. In preparing reports,
especially those reports which are used in typewritten form for limited
distribution, there is a tendency to accompany the typewritten report
with charts on very large sheets of paper, bulky and inconvenient to
handle. Sometimes the scales of these accompanying charts are so
large that the reader is puzzled to get clearly in his mind what the whole
chart is driving at. There is a possibility of making a simple chart on
such a large scale that the mere size of the chart adds to its complexity
by causing the reader to glance from one side of the chart to the other
346
GRAPHIC METHODS
DEEP HOLES IN THE ROAD
151 ft iS %
TUNNEL
SHARP TURN AND ASCENT
& IHJ ft iS B
SHARP TURN AND DESCENT
£ dd ft t:(? JIB
SERPENTINE
IOAI ONSUITAIU FOR CARS
RAILWAY CROSSING
IAKCEROUS ROAD CROSSINC
Courtesy of "Motor"
Fig. 240. International Road Signs that Are Being Erected on the Highways of Japan
by the Nippon Automobile Club
Any conventional symbols or signals adopted for use in graphic work should be as clear and suggestive as it
is possible to make them. The above illustration is shown here as an admirable example of good prac-
tice in the making of graphic symbols
in trying to get a condensed visualization of the chart. There are
relatively few curve charts which cannot be presented for report pur-
poses on paper 8% by H inches, the commonest size used for a type-
writer. Though the placing of a chart on paper of typewriter size
requires more care than is necessary if a very large sheet of paper is used,
the resulting chart is frequently more easy to interpret than it would
be if made to a larger scale.
A warning seems justifiable that the background of a chart should
not be made any more prominent than actually necessary. Many
charts have such heavy co-ordinate ruling and such relatively narrow
lines for curves or other data that the real facts the chart is intended to
portray do not stand out clearly from the background. No more co-
ordinate lines should be used than are absolutely necessary to guide
the eye of the reader and to permit an easy reading of the curves. Too
A FEW CAUTIONS
347
many magazine articles and transactions of scientific societies contain
charts which are reproduced direct from finely ruled co-ordinate paper
and show all of the lines of the co-ordinate paper in the finished illus-
tration. Co-ordinate ruling does not appear prominently on most
original charts because -the ruling is usually printed in some color of ink
distinct from the curve itself. When, however, a chart is reproduced
in a line engraving the co-ordinate lines come out the same color as the
curve or other important data, and there may be too little contrast to
assist the reader.
Curves are sometimes shown plotted vertically when a horizontal
arrangement could be used without any difficulty. There seems to be no
IQIO
, Cylinder Bore
/O% SOT* "SO% -4ofc Soft f>O% 7O/° 8O/9 9O/°
1911
w~
1
^
1912
Ij
*\l
n
«*•
I
1913
w
a
>
£
^?
fc
1910
I9M
1912
1910
1911
1912
1913
Fig. 241
There is i
reader
becau
Valve Arrangement >-. „,
/0% 2O% 30% +0% &0/V 60% T07» QO/o 9O/O
I
1
y
\
\
I
]
^
7
$
n
A
f*i
^
v^
^
,0?. ,0% ,$"<%%" ^/te%e ** «o7- *°?>
1
y
i
^
S;
I
i—
1
V
^
\
\
/
1
[
Courtesy of "Motor"
. Comparison of American Automobiles for Four Years, in Cylinder Bore,
Valve Arrangement, and Ignition System
10 necessity for plotting curves in the vertical position shown here for it is only confusing to the
. These curves cannot be read conveniently even by turning the book to read from the left
se some of the type would then be upside down. See Fig. 242
348
GRAPHIC METHODS
real reason why Fig. 241 should have the curves arranged in the ver-
tical direction. The vertical arrangement confuses the reader until
he ascertains how the curves may be read by turning the book so that
the curves may be read from the left in their proper position.
Fig. 242 shows the data of Fig. 241 plotted in standard manner
Fig. 242 is also of interest because it shows curves plotted from only
a few points for each curve. Though one may be tempted to use
some other method than curve presentation when only few points
PferCent
1OO
PerCent
100
90
8O
TO
60
50
30
10
3-9
PerCent
100
90
BO
70
eo
30
1O
90
8O
70
60
50
30
2O
10
1910 'II '12 '13 1910 'II '12 '13 I9IO 'II '12 '13
Cylinder Valve Ignition
Bore Arrangement Systems
Fig. 242. Comparison of American Automobiles for Four Years, in Cylinder Bore,
Valve Arrangement, and Ignition System
The standard arrangement of the curves on this chart permits easy reading. Notice that curves are per-
fectly feasible as a method of presentation even though there are only a few points available for each curve
A FEW CAUTIONS
349
for a curve are available, it can be seen that even if there were only
three points instead of four in Fig. 242, the curve would still be valu-
able to convey the desired information. In Fig. 53 and Fig. 54 methods
are shown by which charts which are essentially curve charts may be
drawn even though there are available only two points for each curve.
1907
'Surplus
Shortage
I9O8
•Surplus
Box Cars
/III Can,
100,000
WO.OOO ZOO.OOO
so.ooo
100.000 200.000 300.000 400.000
American Railway Association
Fig. 243. Freight-Car Shortage and Surplus in the United States for Four Years,
1907 to 191 1, Inclusive
The horizontal bars here are so numerous and are placed so close together that the charts have practically
the general form of curves drawn vertically instead of horizontally. It would seem just as well to repre-
sent the data by real curves drawn with the standard horizontal arrangement
When curves become as widely understood as the bar method of
presentation, it will be found that curves can be used advantageously
in almost every case where it is now common to use either vertical
or horizontal bars.
In Fig. 243 the horizontal-bar method has been elaborated so that
the resulting chart has practically the general effect which would
be obtained by a curve chart. The reader who wishes to read Fig.
243 in the form of curves is, however, forced to turn the book so that
he may see the chart froin the left with the curves running in a generally
horizontal direction. The data would likely be just as well understood
by railroad men if shown by real curves drawn in the standard manner.
350
GRAPHIC METHODS
1
18
1896
9718
7898
9.9 19
1900
01 IV
1902
mw
1904
05 19
1906
)7 19
1908
W 19
1910
11
dK
AA
r^*"^
At
/
/
•fft
/
?fl
/
~~^t
r
f
36
/
/
"i4
/
32
/
A
30
J
fS*^
/
28
tc '
/
Zb —
New York Times Annalist
Fig. 244. Average per Capita in the
United States of Total Savings-bank
Deposits
At first glance the impression is that Americans are
growing rich very rapidly. Yet total deposits
per capita have not doubled in the sixteen years
shown. If the bottom line of the chart were at
the zero of the vertical scale, an entirely different
impression would be given. See Fig. 245
At numerous places through-
out this book criticisms have
been made of curves and charts
in which no zero line for the
vertical scale was shown on the
chart. Though this subject has
been mentioned elsewhere it seems
best to show here a few examples
on the same general argument.
In Fig. 244 the first glance im-
pression that savings-banks de-
posits have increased with great
rapidity is not entirely confirmed
when it is noticed that the left-
hand scale does not begin anywhere
near zero. It is nearly always
possible to make a chart so that
the zero of the vertical scale will show. Usually, of course, the zero
line is at the bottom of the chart unless there are negative quantities
so that the curve crosses over the zero line and extends below it.
In all cases the zero line can be made a heavy line. If the curve should
extend below the zero line the width of the zero line should be so
great that the reader will be cer-
tain to interpret the chart from
the zero line rather than from
the bottom line of the chart it-
self.
It sometimes happens that the
data for a chart involve high numeri-
cal figures so that a large amount
of space must be used if the zero
line of the vertical scale is to be
shown in the final illustration. In
such a case, the bottom of the chart
may have a wavy line as seen in
Fig. 245 which portrays the same
data as Fig. 244. Fig. 244 could
have been extended so that the bot-
tom line would be the zero line if a
$
18
1896
971&
1898
99 1»
J900
91 19
1902
03 19
1904
05 W\
1906
>7 19
1908
99 19
1910
tl
dfi
AA
^
It
J
/
4£
An
f
J
9O
>
^
f
4
?fi
/
J
9J
i
^B
i**
c
/^
32—
Oft
f
/
28
i
\
£
60—
Fig. 245. Average per Capita of Total
Savings-bank Deposits in the United
States
Whenever possible a chart containing curves should
be so drawn that the zero of the vertical scale
appears in the chart. If the zero line is not
shown on the chart, that fact should be indicated
by a wavy line at the bottom warning the reader
that interpretation must be made from the ver-
tical scale and not by visual measurement from
the bottom line of the chart
A FEW CAUTIONS
351
Indicating INCREASE In Deaths from Degenerative Diseases and DECREASE fnm Tuberculosis
188O
189O
191O
Elmer Rttlenhowe, In the New York Times
Fig. 246. Comparison of Death Rates in the United States, Showing Reduction in
Death Rate for Tuberculosis and Increase in Death Rate for Degenerative Dis-
eases
The chart gives the impression of very rapid decreases and increases, chiefly because the bottom line is
not at the zero of the vertical scale. The figures used for the vertical scale are rather small in size and
the rapid reader is not likely to notice that the scale does not begin at zero. Compare Fig. 247 and Fig.
248
somewhat greater amount of photographic reduction had been used
in making the line engraving or if the proportions between the hori-
zontal- and vertical-scale distances had been changed somewhat.
There is really no necessity for using the wavy line for the bottom
of Fig. 245 since the chart would have been better made with the
zero line showing the bottom. Fig. 245 will serve, however, as an
example to illustrate how the wavy line can be drawn to any chart
where it is really inconvenient to extend the chart itself so that the
zero line may show.
Death Rate
Per 1O.OOO
•40
i860
1Q90
•Tuberculosis
I91O
Degenerative Diseases
(Heart, Kidney, etc.)
Data of Elmer Rtttenhouse
Fig. 247. Comparison of Death Rates in the United States, Showing Reduction in
Death Rate for Tuberculosis and Increase in Death Rate for Degenerative Dis-
eases
This chart is made from the same data as Fig. 246. Here the zero line is shown and the changes in death
rate appear much less rapid than they do in Fig. 246. See also Fig. 248
352
Fig. 246 gives another example where neglecting to show the zero
line may cause an entirely erroneous impression regarding the facts
which the chart is intended to bring out. The failure to show the
zero line at the bottom of a chart is so common a fault, found in nearly
all publications, that some typical examples are shown here in the
hope that a bad practice may be somewhat reduced.
Fig. 247 gives the data of Fig. 246 redrawn so that the zero line
is shown at the bottom of the chart. It is believed that this illustra-
tion will prove conclusively how great an error may be made if charts
are read hastily on the assumption that the bottom line of the chart
is the zero line. Since some persons are almost sure to read a chart
from the bottom line, it seems desirable that all charts should be so
made that the reader may interpret from the bottom line as a zero
line, or else receive positive warning that he should not do so.
Indicating INCREASE In D<»fh$ frnrn Degenerative Diseases and DECREASE fan Tuberculosis
Data of Elmer
Fig. 248. Comparison of Death Rates in the United States, Showing Reduction in
Death Rate for Tuberculosis and Increase hi Death Rate for Degenerative Dis-
eases
This illustration is identical with Fig. 246 except that here a wavy line is used at the base showing that the
bottom of the chart is not at the zero of the vertical scale. It is always desirable to have the bottom line
at zero. If that is not possible the wavy line should be used as a warning to the reader
Though there is no necessity for showing Fig. 246 without having
a zero line at the bottom of the chart, Fig. 248 is presented here to
prove how easy it is to make a wavy line at the bottom of a chart if
there should be any real reason why the chart cannot be made so
as to include the zero line of the vertical scale. Fig. 248 is exactly
the same as Fig. 246 except that the wavy line is used instead of the
straight line at the bottom.
The beginner in curve plotting and in curve reading is apt to be
somewhat puzzled by the different effects which may be obtained by
changing the ratio between the vertical scale and the horizontal scale.
It is difficult to give any general rules which would assist in overcoming
the beginner's confusion. Ordinarily the best way to get facility
in making the proper choice of vertical and horizontal scales for plot-
A FEW CAUTIONS 353
ting curves is to take one set of data and plot those data in several
different ways, noticing the changes which the different scales selected
give in the proportions of the chart. Just as the written or spoken
English language may be used to make gross exaggerations, so charts
and especially curves may convey exaggerations unless the person
preparing the charts uses as much care as he would ordinarily use to
avoid exaggeration if presenting his material by written or spoken
words. Most authors would greatly resent it if they were told that
their writings contained great exaggerations, yet many of these same
authors permit their work to be illustrated with charts which are
so arranged as to cause an erroneous interpretation. If authors and
editors will inspect their charts as carefully as they revise their written
matter, we shall have, in a very short time, a standard of reliability
in charts and illustrations just as high as now found in the average
printed page.
Fig. 249 shows an interesting application of the use of charts to
corporation reports. The back page of the annual report of the Ameri-
can Telephone and Telegraph Company has the proportions seen in
Fig. 249. As a report to stockholders is intended to be as optimistic
as possible within the limits of truthfulness, there can scarcely be any
criticism that the chart was so made that the growth in business was
shown on the long direction of the page instead of on the short dimen-
sion of the page. The chart in Fig. 249 is simple to understand, and
probably very few stockholders would have any difficulty in making a
fairly accurate interpretation. For the annual report of a corporation,
it is likely that the vertical-bar method of Fig. 249 is preferable, from
an advertising standpoint, to a smooth curve like that shown in Fig. 250.
One special point relating to Fig. 249 is worthy of mention. At the
bottom of the chart will be noticed the statement that the figures re-
corded are those of "January 1st of each year". This statement may
lead to an erroneous conclusion on the part of the reader, for he may
feel that the difference in height between the bar marked 1911 and that
for 1912 shows the number of telephones installed during 1912, when,
in reality, it shows the number of telephones installed during 1911,
since the bars represent the number of 'phones installed to the first of
January of each year. If the statement at the bottom of the chart had
been made "December 31st of each year" there would be no danger
of misinterpretation. If the statement were made for December 31
it would, of course, be necessary to change the numbers at the bottom
6,700.000
6,600,000
6,500,000
]
C
S
S
i
W
n
tat
!
.11
E
&
Jan
on
SH
&
0
I
1
[.
ua
to
0\
S(
3N
1
3
i,
y i
ee
VI
H
ME
J
0
1
, I
ch
D
NC
31
CT
1
i9
8
512
14
I
-
IAGRAM
1 THE GROWTH IN
SERS' STATIONS
ED TO THE SYSTEM
OF THE
TELEPHONE
IPANIES
FROM
76— JAN. 1,1912.
6,400,000
6,300.000
1 6,200,000
6,100.000
6,000.000
5,900,000
6,800.000
5,700.000
5,600,000
5,500,000
5onn rwv»
5100 000
5 OOO OOO
A QOO OOO
4,800.000
4,700.000
4,600,000
4,500.000
th
of
Jni
ers
the
ed
\v
T
SI
as
ota
ate
on
F
i.
i B
op
ell
ula
Te
lor
lap
0
hoi
t
\a
te
4,400,000
4.300.000
4,200,000
4,100,0000)
4,000.000g
3,900,000 fl
3.800.000 <
3,700.0000)
3,600.000.
3,600.000^
3,400,000 UJ
3,300.000 1
3,200.0000
3,100.000g
3,000,0003
2,900,000OT
2,800,000 g
2,700,000
2,600.000 £
2.500.000 0
-2.400.000 2
2,300,000z
2,200,000
2,100.000
1876
18
78
1C
80
j— i
IS
p|
82
H
IE
-
84
IE
86
JA
1
IE
NL
1
88
1AI
J
18
3Y
|
90
Is
18
T
J
92
OF
It
E
J
94
AC
]
U
:H
i
96
Y
]
18
EA
I
98
R.
E
IS
-
00
-
02
19
1
-
04
-
-
190
6 19
08 19
10 1
2,000.000
1,900,000
,800.000
,700.000
,600.000
,500.000
,400.000
,300,000
,200.000
1,100,000
1,000,000
900.000
800.000
700,000
600,000
600,000
400.000
300,000
200.000
100,000
2 °
American Telephone & Telegraph Co.
Fig. 249. The Number of Subscribers' Stations Connected to the System of the Bell
Telephone Companies
This illustration .was shown on the back cover of the 1911 annual report to stockholders of the American
Telephone & Telegraph Company. For the average stockholder the vertical bars would probably be
understood more readily than the curve shown in Fig. 253. Compare with Fig. 250 and Fig. 251
6,700,000
6,600,000
6,500,000
6,400,000
6,300,000
6,200,000
6,100,000
6,000,000
5,900,000
5,800,000
5,700,000
5,600,000
5,500,000
5,400,000
5,300,000
5,200,000
5,100,000
5,000,000
4,300,000
4,800,000
4,700,000
4,600,000
4,600,000
4,400,000
4,300,000
4,200,000
4,100,000
4,000,000
3,900,000
3,800,000
3,700,000
3,600,000
3,500,000
3,400,000
3,300,000
3,200,000
3,100,000
3,000,000
2,900,000
2,800,000
2,700,000
2,600,000
2,500,000
2,400,000
2,300,000
2,200,000
2,100,000
2,000,000
1,900,000
1,800,000
1,700,000
1,600,000
1,500,000
1,400,000
1,300,000
1,200,OCO
1,100,000
1,000,000
900,000
800,000
700,000
600,000
500,000
400,000
300,000
200,000
100,000
0
Fig. 250. The Number of Subscribers' Stations Connected to the System of the Bell
Telephone Companies, December 3ist of Each Year
The curve permits quicker and more accurate interpretation than the vertical bars but unfortunately curves
are not readily understood by as many people. Note that the date on which the telephones are recorded
is here specified as December 31st instead of as January 1st. Compare Fig. 251
355
DIAGRAM
SHOWING THE GROWTH IN
SUBSCRIBERS' STATIONS
CONNECTED TO THE SYSTEM
BELL TELEPHONE
COMPANIES
FROM
JAN. 1, 1876— JAN. 1, 1912.
On January I, 1912. thera wu on. Ball Telophono
Station to each 14 of the Total Population of the
United States.
356
GRAPHIC METHODS
0 n
r- s w
2 oUJ 3
i^r.o
o
CO
D
(0
LU
00
o
TT6T PQ
OT6T 0>
~-
006T
~0 -««
fl-S o
|
T8,
6i.
S i a
.tn O «1 y
fl1!^
., *J— O
§ §
W)
A FEW CAUTIONS 357
of each vertical bar so that they would appear in each case one less than
the figures given. With Fig. 249 as it is, the 1908 bar shows a great
increase over 1907 and the reader is quite justified in wondering how
it happened that a greatly increased number of telephones were installed
during a panic year. From the chart as shown the reader is not- likely
to realize that 1908 is getting credit for the telephones installed during
1907, which happened to be a very prosperous business year. Having
the data recorded as of December 31 each year overcomes the difficulty
and makes certain that no false impression can be obtained.
Fig. 250 shows the data of Fig. 249 plotted as a smooth curve. For
a trained class of readers the curve presentation is preferable to the bar
presentation, for it permits seeing the fluctuations which have occurred
from year to year more easily than they can be seen by glancing from
bar to bar in Fig. 249. Within a few years it is probable that curves
will be so well understood that a report to stockholders could best be
made using the method of Fig. 250 instead of the method of Fig. 249.
In order to show the different impressions which may be had if
various proportions between the horizontal and vertical scales are used,
Fig. 251 has been plotted from the same data as Fig. 249 and Fig. 250.
For Fig. 251 an assumption was made that the chart would be printed
on exactly the same size page as was used for Fig. 249. The scales for
Fig. 250 were, however, arranged in the other direction on the page and
the co-ordinate ruling was made so that some space would be allowed
for extension of the curve in future years. As seen from Fig. 251 the
growth in the telephone business does not appear nearly so rapid as
would be thought from observing Fig. 250. Each of these charts is,
however, plotted to exact scale and the difference in the impression
obtained is caused only by the proportions of the vertical and the hori-
zontal scales. The appearance of less rapid growth in Fig. 250 is
assisted somewhat by the fact that the large-type title of the chart is
arranged horizontally instead of in the form of a square as seen in Fig.
250. The heavy black type with much greater spread horizontally
than vertically tends to overshadow the curve itself and causes for the
curve a more distinctly horizontal impression than would otherwise
be obtained. A person reading charts must take great care that he
does not give too much weight to the actual appearance of the curve
on the page, instead of basing his conclusions on the percentage increase
or decrease as judged from the figures of the vertical scale. The proper
choice of scales for curve plotting is largely a matter of judgment, and
358
GRAPHIC METHODS
'/.. \
Courtesy of the Groller Society
Fig. 252. An Optical Illu-
sion
The black line at the left appears
longer than the one at the right.
The two lines are, however, of
the same length
the judgment can be trained very greatly if it is kept in mind to examine
every curve chart which comes to one's attention to see whether the
vertical and horizontal scales have been so selected that the chart gives
\ ..•* a fair representation of the facts.
The English language has so many
words with double meaning and so many
words for which the shades of meaning
are rather indistinct that there are really
many more chances of false impression
from the written or spoken language than
there are from the data expressed in graphic
form. Nevertheless, a few examples of op-
tical illusions are shown here so that the
reader may have some idea of those peculiar
things which may enter in to cause strange impressions if charts do not
receive some degree of preliminary care and final inspection. Though
many of the effects seen in Fig. 252, Fig. 253, Fig. 254, Fig. 255, and
Fig. 256 are not likely to appear in
ordinary chart work, they may not-
withstanding cause difficulty in some
kinds of very large wall exhibits. Fig.
254, in particular, shows an effect which
is to be avoided where large quan-
tities of black ink are used. In a
recent series of charts comparisons were
made between different white squares,
surrounded in each case by a black
border practically as wide as the square at the center. It is not likely
that a reader seeing a series of black squares with white centers of dif-
ferent size would be able to judge correctly the relative size of the
white squares at the center.
Fig. 256 shows some of the difficulties
which may be encountered if an attempt
is made to present data by comparing the
relative heights of pictures of the human form.
There are few people who will believe until
they make measurements that the figure
Courtesy of the Grolier Society
Fig. 253. An Optical Illusion
The left-hand arrangement looks wider than
it is high while the right-hand arrange-
ment looks higher than it is wide. On
each side the height is the same as the
width
Courtesy of the Groller Society
Fig. 254. An Optical Illu-
sion
The white square appears larger of the girl in Fig. 256 is really of greater
&* the tW° length than that of the policeman. The illusion
A FEW CAUTIONS
359
is caused chiefly by the perspective lines of the drawing which force
one to estimate relative height to a certain extent by the number of
perspective lines intersected instead of by the actual size of tlie black
pictures.
Before charts are sent to an engraver to
have plates made for printing it is wise to
have each chart run the gauntlet of a series of
questions, so that the time of the person doing
the checking may be saved and also that the
points more frequently overlooked may be
thoroughly considered' in each case. Below are
given a series of questions which may be found
convenient to anyone having charts to prepare.
This list is not by any means complete, and
the questions are given here as general sugges-
tions only. The person checking a chart simply
reads the ques-
tions one by one
from the book,
and then care-
fully observes
the chart to see
whether it comes
up to the stand-
ard. Whenever
possible it is well „
to have the chart
of the Grolier Society
An Optical
Illusion
SOTT1P r^e commns appear bent. The
- ' left-hand pair seem closest
person Other than at the ends, while the right-
hand pair seem closest at
the One Who drew the center. The sides of the
.. T j- columns are really straight
it. In every edi- and paraiiei
torial office the
~ . , T11 fact is recognized that one proof-reader
Fig. 256. An Optical Illusion °
The policeman appears much taller than the Will find important errors that Were
overlooked by another reader equally
expert. Further, a mind much occupied
with an idea may often fail to see important gaps in its statement,
verbal or graphic, until perhaps they are noted by someone less familiar
with the subject. Two points of view are always better than one.
Courtesy of the Grolier Society and of Popular Mechanics
360 GRAPHIC METHODS
CHECKING LIST FOR GRAPHIC PRESENTATIONS
1. Are the data of the chart correct?
2. Has the best method been used for showing the data?
3. Are the proportions of the chart the best possible to show the
data?
4. When the chart is reduced in size will the proportions be those
best suited to the space in which it must be printed?
5. Are the proportions such that there will be sufficient space for
the title of the chart when the chart has been reduced to final printing
size?
6. Are all scales in place?
7. Have the scales been selected and placed in the best possible
manner?
8. Are the points accurately plotted?
9. Are the numerical figures for the data shown as a portion of the
chart?
10. Have the figures for the data been copied correctly?
11. Can the figures for the data be added and the total shown?
12. Are all dates accurately shown?
13. Is the zero of the vertical scale shown on the chart?
14. Are all zero lines and the 100 per cent lines made broad enough?
15. Are all lines on the chart broad enough to stand the reduction
to the size used in printing?
16. Does lettering appear large enough and black enough when
seen under a reducing glass in the size which will be used for printing?
17. Is all the lettering placed on the chart in the proper directions
for reading?
18. Is cross-hatching well made with lines evenly spaced?
19. Can Ben Day work be used advantageously instead of cross-
hatching?
20. Do the Ben Day shadings selected have sufficient contrast?
21. Are all instructions for Ben Day work given so that it will be
impossible for the engraver to make a mistake?
22. Are dimension lines used wherever advantageous?
23. Is a key or legend necessary?
24. Does the key or legend correspond with the drawing?
25. Is there a complete title, clear and concise?
26. Is the drafting work of good quality?
A FEW CAUTIONS 361
27. Have all pencil lines which might show in the engraving been
erased?
28. Is there any portion of the illustration which should be cropped
off to save space?
29. Are the instructions for the final size of the plate so given
that the engraver cannot make a mistake?
30. Is the chart in every way ready to mark "O.K"?
The English language has a grammar with hundreds of detailed
rules concerning almost every possible construction. Though graphic
presentations are used to a very large extent to-day there are at present
no standard rules by which the person preparing a chart may know
that he is following good practice. This is unfortunate because it
permits every one making a chart to follow his own sweet will. Many
charts are being put out to-day from which it would seem that the person
making them had tried deliberately to get up some method as different
as possible from any which had ever been used previously. Anyone
of us would be thought of as a freak instead of as a genius, if he tried
to invent his own constructions for the English language and to place
words in some order never before seen, yet many persons are doing
something akin to this when they attempt to present data by some
new and outlandish method of charting. Below are given a few rules
which may be of assistance toward getting graphic presentations more
on a standard basis so that they may be instantly read. These rules
are included here simply as suggestions, and they should be considered
as only tentative until such time as definite rules have been agreed
upon and sanctioned by authoritative bodies.
RULES FOR GRAPHIC PRESENTATION
1. Avoid using areas or volumes when representing quantities.
Presentations read from only one dimension are the least likely to
be misinterpreted.
2. The general arrangement of a chart should proceed from left to
right.
3. Figures for the horizontal scale should always be placed at the
bottom of a chart. If needed, a scale may be placed at the top also.
4. Figures for the vertical scale should always be placed at the left
of a chart. If needed, a scale may be placed at the right also.
5. Whenever possible, include in the chart the numerical data from
which the chart was made.
362 GRAPHIC METHODS
6. If numerical data cannot be included in the chart, it is well to
show the numerical data in tabular form accompanying the chart.
7. All lettering and all figures on a chart should be placed so as to
be read from the base or from the right-hand edge of the chart.
8. A column of figures relating to dates should be arranged with the
earliest date at the top.
9. Separate columns of figures, with each column relating to a
different date, should be arranged to show the column for the earliest
date at the left.
10. When charts are colored, the color green should be used to
indicate features which are desirable or which are commended, and red
for features which are undesirable or criticized adversely.
11. For most charts, and for all curves, the independent variable
should be shown in the horizontal direction.
12. As a general rule, the horizontal scale for curves should read
from left to right and the vertical scale from bottom to top.
13. For curves drawn on arithmetically ruled paper, the vertical
scale, whenever possible, should be so selected that the zero line will
show on the chart.
14. The zero line of the vertical scale for a curve should be a much
broader line than the average co-ordinate lines.
15. If the zero line of the vertical scale cannot be shown at the
bottom of a curve chart, the bottom line should be a slightly wavy
line indicating that the field has been broken off and does not reach to
zero.
16. When curves are drawn on logarithmically ruled paper, the
bottom line and the top line of the chart should each be at some power
of ten on the vertical scale.
17. WThen the scale of a curve chart refers to percentages, the line
at 100 per cent should be a broad line of the same width as a zero line.
18. If the horizontal scale for a curve begins at zero, the vertical
line at zero (usually the left-hand edge of the field) should be a broad
line.
19. When the horizontal scale expresses time, the lines at the left-
and right-hand edges of a curve chart should not be made heavy, since
a chart cannot be made to include the beginning or the end of time.
20. When curves are to be printed, do not show any more co-
ordinate lines than necessary for the data and to guide the eye. Lines
34 -inch apart are sufficient to guide the eye.
A FEW CAUTIONS 363
21. Make curves with much broader lines than the co-ordinate
ruling so that the curves may be clearly distinguished from the back-
ground.
22. Whenever possible have a vertical line of the co-ordinate ruling
for each point plotted on a curve so that the vertical lines may show the
frequency of the data observations.
23. If there are not too many curves drawn in one field it is desirable
to show at the top of the chart the figures representing the value of
each point plotted in a curve.
24. When figures are given at the top of a chart for each point in a
curve, have the figures added if possible to show yearly totals or other
totals which may be useful in reading.
25. Make the title of a chart so complete and so clear that misinter-
pretation will be impossible. ^^^^ M^-^Ut [c4 /L
The American Society of Mechanical Engineers has invited about
fifteen of the societies of national scope in America to co-operate in a
Joint Committee on Standards for Graphic Presentation. The societies
included are largely societies whose members have extensive use for
graphic presentation in their daily work. One member from each
society will be on this committee. It is hoped that the committee will be
able to recommend a small number of brief and simple rules which may
be used as a sort of grammar by persons who have graphic presentations
to prepare and to interpret. Reports from this joint committee should
be watched for so that any rules which may be agreed upon may be
put into effect as soon as possible.
Improvements in the means of transportation by water, rail, auto-
mobile, wire, and wireless in recent years have caused a tremendous
increase in the amount of printed matter and the amount of statistical
material read by the average person. Newspapers and magazines are
daily presenting more and more statistical information. If we study
the subject even a little, it will be seen that each of us deals daily with a
vast number of facts of a quantitative nature which could preferably
be presented in graphic form. When graphic methods are more widely
used for portraying quantitative facts, there will be a tremendous gain
to accuracy of thought as well as a great saving of that most valuable
thing in the world — time.
THE END
INDEX
Abbreviations for chart work, 345, 346
Accidents, as affected by daylight, 140
in industrial plants, 144, 145
on railroads of United States, 134, 135
Accountants, viewpoint of, 300
Accuracy and significant figures, 326
Acker, Merrall & Condit Co., 116
Adding machines, pocket, 325
Advertising, bead maps for, 253
maps for, 238, 239
use of curves for, 77, 78
Allen, William H., 250
American Jersey Cattle Club, 278
American Machinist, 335
American Railway Association, 349
American Review of Reviews, 46, 47, 229, 231
American Society of Mechanical Engineers,
ii, 31, 52, 54, 122, 363
American Statistical Association, 167, 176,
197
American Telephone & Telegraph Co., 5,
179, 240, 309, 353, 354, 355, 356
Analysis of sales, 188
Angle of a cumulative curve, 150
of a curve, 131
Annalist, the, see New York Times Annalist
Annual reports, corporation, 307
Apples, price curves of, 127, 128, 129
Arithmetically ruled co-ordinate paper, 132
Atlas of the U. S. Census, see Statistical
Atlas
Atomizer for spraying ink, 57
Authorization for curve recordsr 284
Automobile exports of United States, 41, 43
factory records, 263
factory schedule curves, 150
sales records, 255, 264
Automobiles, comparison of, 347, 348
Averages, moving, 97, 283
progressive, 153
weighted, 103
Babson, Roger W., 120, 121
Bacteria in river water, 20
in river water at varying depths, 85
Bald Eagle Valley Railroad, 67
Bar diagrams versus curves, 310
Bars combined with a curve, 54
certain made prominent, 29, 30
for use in comparison, 22
horizontal, 4
horizontal, representing time, 53
vertical, 46, 47
vertical, for components, 138
Bead maps, 251
Beads for map use, 247, 248
for statistical charts, 207
Bell Telephone systern, 353, 354, 355, 356
Ben Day shading, 216, 220, 331, 332
shading on maps, 209
work, 331, 332
Bertillpn, 220
Biologists, use of curves by, 203
Biometrika, 202
Blue-printing, 328
cards, 259, 261
curve cards, 291, 296
machines, 261, 296
Boards for pin records of costs, 191, 192
Bonus earned chart, 52, 54
Boston Elevated Railroad, 4
Boston Globe, 212
Boston Health Department Report, 30, 109
Bowley, Arthur L., ii, 98
Breaks in drawings, 190
Bridges, drawing, upon photographs, 209
Brotherhood of Railroad Trainmen, 103
Building construction in United States, 120,
121
Buildings, maps for showing height of, 220
Bureau of Railway Economics, 257
Butter-fat curves, 279
Camera lenses, 330
Cameras, motion picture, for time study, 50
Campaigns, political, 338
Car-floats, dispatching, 61, 62
Cars, shortage and surplus, 349
Cardboard for blue-printing, 259, 261
models, 336
385
366
GRAPHIC METHODS
Card-sorting machines, 322
Cards for blue-printing, 259, 261
for curve-plotting, 256
for curves, 275
for tabulating machines, 320
Cards, information, 287
Carson, John M., 326
Cartoon drawings, 20, 21
Cattle distribution in United States, 215
Cautions, a few, 344
Celluloid-covered tacks for maps, 247, 248
Celluloid, erasing drawings from, 210
flags for maps, 247
for drawings with maps, 210
for mounting maps, 210
tacks for writing, 247, 248
Cement plants in United States, 243
price of for thirty years, 77
Census Abstract, 218
Census Atlas of United States. See Statis-
tical Atlas
Census-Office methods, 320, 321
Census tabulating card, 320
Charts, best size for, 345
in political campaigns, 338
on walls, 306
Checking list for graphic work, 359, 360
Chicago Burlington & Quincy Railroad,
40
Chicago pin map for population, 246
Chicago telephone rates, 126
Choice of scales, 352
Cincinnati, homes of factory workers, 214
Circle and sectors, 5
Circles compared, 36, 37
Clamps for hanging maps, 232
Cleveland Plain Dealer, 92
Cloak and suit industry in New York, 166
Coals, comparative value of, 88
Coloring maps, 209
Color-printing, 5, 331
Colors for chart work, 57
Columns of figures, order for, 45
Combined curves, 125
Commerce of the United States, 70, 71
of the world, 76
Commercial geography, 21
Commercial Museum of Philadelphia, 70,
74, 76, 112
Commission on Economy and Efficiency,
33,34
Comparisons, 20
involving time, 36
Comparison of curves, 107
Compo-board, 232
Component parts, 1
parts grouped, 33
parts shown by curves, 138
Compound-interest curve, 131
Conjugal condition of population, 9
of population of United States, 168, 169
Construction of giaphical charts, 335
Co-ordinate lines, spacing of, 362
paper, 55
paper for weekly records, 150
paper, universal, 60
ruling, 284
Copper production, 26
Copying drawings, 329
Copyrights on maps, 237
Cork composition for map mounting, 232
Corn crop in United States, 44
planting dates in United States, 213
yield and rainfall, 124
yield per acre in United States, 217
Corporation directors, 289, 298
executives, 28D
financial reports, 307
record department, 292
Correlation, 129, 199
definition of, 199
Corrugated straw-board for map pins, 191
Cost analysis by pin boards, 191, 192
of handling freight, 184, 188, 192"
Cotton goods, production and export, 74,
75
Cotton production, 22
production and export of United States,
41
Country Gentleman, 213, 215, 232
Cows, individual record curves for, 278, 279
Crayons for coloring maps, 57, 221
Crayons, paraffin, 57
Crests and valleys of curves, 79
of curves, 79
Crop Reporter, 100
Cross-hatching, 9
Cross-index of curves, 291
Croton water-supply curves, 160
Cumulative curves, 149
frequency curves, 174, 176, 177, 182, 184
Cunningham, Wm. J., 132, 134, 135, 136
Curtis Publishing Co., 238
Curve comparison, 107
Curve plotting, 47, 69, 84
Curves and vertical bars, 47
for the executive, 254, 288
interpretation of, 357
inversely related, 126
plotted on cards, 259, 275
INDEX
367
Curves and vertical bars, reading of, 30£
serial numbers for, 287
shown by reflectoscope, 303
versus bar diagrams, 310
Cycles of curves, 97, 283
in curves, 97, 283
Cylindrical lenses, 330
Data, 7, 42, 88, 126, 178, 204, 243, 333
Data for curves, on face of chart, 80, 258
for curves, shown on chart, 80, 258
included in a chart, 24, 25, 26
Dates, position of, in curve charts, 72
Davenport, C. B., ii, 164, 165
Davis, Pierpont V., ii
Day & Zimmermann, 296, 305, 306
Death rates in United States, 174, 351
Decreases shown graphically, 30
Degenerative diseases, 351
Department of Agriculture Field Service,
232
Dependent variable, definition, 84
Depressions, financial, 104
Dimension lines, 5, 148
Directors of corporations, 289, 298
Dispatching charts for trains, 61, 62, 67
Display fixtures for curves and maps, 305
fixtures for maps, 233
Distribution charts, 165
curves, 165
of wealth, 197
Dividends and earnings of Steel Corpora-
tion, 313, 314
Dixon, Frank Haigh, 115
Dodd, Mead & Co., 250
Dodge's Advanced Geography, 22
Double co-ordinates for curves, 95
scales for curves, 95
Draft curves for water consumption, 160
Drawing ink, 46, 47, 276
Dreyfus, Edwin D., 117, 118
Drinking, reduction in, 345
Droege, John A., Freight Terminals and
Trains, 48
Earnings and dividends of Steel Corpora-
tion, 313, 314
of college graduates, 111
of wage earners in U. S., 180, 181
Earthwork curves, 163
Edison Company, New York, 108, 138,
140, 146
Eggs, price of, 100
Elderton, W. P. & E. M., ii
Election returns, methods of giving, 341
Engineering Magazine, 12, 14, 17, 18, 116,
125, 246
Engineering News, 87
Engineering Record, 79, 119, 209, 210
Equitable Life Assurance Co., 174, 175
Errors in comparison, 20
Ewerbeck, Dr., 225
Exaggeration due to scales used, 353
Examination marks, charting, 205, 206
Executive control curves, 254, 288
Executives of corporations, 289
Exhibition board, 232
Exports and imports of United States, 37
Exports from the United Kingdom, 98
Eye-catchers, 25, 26, 27, 123
Factory, 147, 155, 180, 256
Fan tests, 335
Farm-land values in United States, 218
Farwell, E. S., 335
Figures included in a chart, 27
misleading, 326
significant, 326
Files for curve cards, 289, 291
Financial charts, 104
prosperity curves, 293
reports, corporation, 307
Fire losses in United States, 120, 121
Fisher, Irving, 10
Fixtures for displaying curves and maps,
305
Flags, celluloid, for maps, 247
Flat-top curve-plotting, 256
Flood curves, 77, 79, 119
Food prices in United States, 103
Football games, charting, 212
Foreign trade of United States, 139
Forms, routing printed, 18
Formulas for curves, 202
Frankfurt a.M., Map of, 225
Freeman, John R., 160
Freight-car shortage and surplus, 349
handling, curves for analysis of, 184,
188, 192
service on Illinois Central, 310
service on Union Pacific, 311
traffic density map, 224
train operation, 123
French curves, 201
Frequency curves, 164
Gang punch for cards, 324
Gantt, H. L., 52, 54
Garnett, W., 205, 206
Gasoline costs for motor trucks, 198
368
GRAPHIC METHODS
Gasoline-electric generator advertisement,
78
Gear teeth, strength of, 334
General Electric Review, 78, £39
General methods, 321
Geography books, 22
Gifford, Walter S., 179, 240
Gilbreth, Frank B., 50
Good Housekeeping, 21
Grammar for graphic work, 361
Graphic presentation, rules for, 362
Graphical charts, construction of, 335
Green ink, making line cuts from, 330, 331
Grolier Society, 358, 359
Grouping of component parts, 33
Grooves in cards for filing, 296
Gummed letters, 46
tape for map mounting, 231
Half-tones from pin maps, 235
Handling freight, cost of, 184, 188, 192
Harriman, Mrs. E. H., 250
Harvard Engineering Journal, 337
Harvard University, 212
Harvard University graduates, 251
Hazen and Whipple, 95
Health-department reports, 108
Heating and Ventilating Magazine, 93
Height of university students, 165
Hewes, Amy, 167, 176
Himman, J. J., 114
Hollerith tabulating machines, 229, 230, 231
Holmes, H. W., 208
Horizontal bars, 4
for comparison, 24
representing time, 53
Hull, G. H., 104
Human figure in comparisons, 39
Illinois Central Railroad, 310
Illusions, optical, 358, 359
Imports and exports of United States, 37
Incandescent-lamp tests, 337
Income curves, 197
Income of technical graduates, 204
Increases shown graphically, 30
Independent, the, 21, 38
Independent variable, definition, 84
Index numbers, 100
Indianapolis Department of Health, 114
Indianapolis smoke deposits, 245
Industrial depressions, 104
Industrial Engineering, 117, 118
Infectious diseases shown in contrast, 30
Information cards, 286, 290
Ink, drawing, 46, 47, 276
Internationale Baufach-Ausstellung, 225
Inversely related curves, 126
Inverted curves, 96
Iron Age, the, 110, 119
Irregular curves, use of, 201
Isometric drawings, 333
ruling, 167, 334, 335
Japanese road signs, 346
Jersey Cattle Club, American, 278
Jevons, Stanley, 319
Joint Board of Sanitary Control, 166, 253
Joint Committee on Standards for Graphic
Presentation, ii, 363
Keuffel and Esser Company, 326
Key for charts, 360
King, Willford I., ii, 328
Labeling packages, 90, 91
Lamps, types in use, 138
tests of incandescent, 337
Land value in United States, 218
Lantern slides for election returns, 341
slides in political campaigns, 339
talks in political campaigns, 340
Legend for charts, 360
Lenses, camera, 330
cylindrical, 330
"Less than" basis for frequency curves, 179
Lettering on charts, 26, 82
Letters of appeal for money, 250
gummed, 46
Lighter operation, chart for, 56
Line cuts from pin maps, 234
made from green ink, 330, 331
Line thickness in reduced drawings, 242
Lines connecting different bars, 31
Loans to industrial employees, 156
Locomotive feed-water curves, 159
Logarithmic co-ordinates, 132
paper, 334, 362
ruling, 334
scale for curves, 132
Lorenz curve, 197
Lorenz, M. O., 197
Lubrication cost at a factory, 256
Manufactured products of cities, 23
Map and pin systems, 226
Map copyrights, 237
models, 225
pins, 225
pins used for cost analysis, 192
INDEX
369
Map pins with numbers, 243, 247
presentations, 208
tacks, 225
Maps, coloring, 209
for corporation records, 293
for election returns, 341
for wall use, 225, 229
mounting of, 231
shading, 209
Marx, Guido H., 334
Mass curves, 149
Massachusetts Institute of Technology,
11, 198
Mazda lamps, 337
McAbee, William D., 245
McGraw-Hill Book Co., 335
Mechanical shading, 331, 332
Merchant tonnage of United States, 112,
113
Methods, general, 321
Metropolitan Sewage Commission, 20, 85
Milk-analysis curves, 114
Milk-production curves, 278, 279
Misleading figures, 326
Mode, 165, 170
Models, card-board, 336
solid, 336
"More than", basis for frequency curves,
179
Morgan, J. P. & Co., 15
Motion picture cameras for time study, 50
Motor, 346, 347
Motor trucks, cost for gasoline, 198
cost of operating, 11
Mount Holyoke College, 167, 176
Mounting maps, 231
Moving-average curves, 97, 283
Municipal parades, 343
record departments, 298
Muslin facing for pin boards, 231
Naphtaly, Sam. L., 122
Natural scale for curves, 132
Need for graphic methods, 1
Newark, N. J., public schools, 2
Newburgh, N. Y., report on schools, 24
New York Edison Company, 108, 138, 140,
146
New York municipal parade, 343
New York Public Library, 299, 329
New York Times Annalist, 13, 45, 313, 350
New York Times, 120, 121, 222, 351
Newspaper circulation curves, 92
Nippon Automobile Club, 346
Numbered map pins, 243, 247
Optical illusions, 80, 81, 358, 359
Order of Railroad Conductors, 103
Orders, routing, 19
Organization charts, 14, 15
Orrok, George A., 201
Panics, financial, 104
Parades, charts shown in, 342, 343
municipal, 343
Paraffin crayons, 57
Paris, height of buildings in, 220
Paris, plaster of, 336
Passengers carried on railways, 39
Passenger service on Union Pacific, 312
Payroll curves, 260
record curves, 276
Peaked-top curves plotting, 256
Peaks of curves, 99
Pearson, Karl, 202
Peddle, John B., 335
Pencil lines, erasing, 361
Pennsylvania Farmer, 124, 127, 128
Pennsylvania Railroad, 308
profile of, 213
Percentage scales for curves, 132
Perspective routing charts, 19
Philadelphia Commercial Museum, 70, 74,
76, 112
Philadelphia Transit Commissioner, 245
Philip's Chamber of Commerce Atlas, 26,
27
Philippines, comparative size of, 211
Photographing bead maps, 252
pin maps, 230, 234
Photographs, drawing upon, 209
progress, 49, 50
used with maps, 209
Photostat, the, 296, 330
use of, 329
Pin boards for cost analysis, 191, 192
Pin maps to scale, 246
Pins for map use, 225
for population density on maps, 221
Pipe, cast-iron, 110
Pittsburgh & Lake Erie Railroad, 81, 82
Plant, Thomas G. & Co., advertisement, 233
Plaster of Paris, 336
Plates, weight of steel, 333
Pneumonia, deaths from, at different ages,
172, 173
Polar co-ordinates for curves, 80
Political campaigns, charts in, 338
Popular Science Monthly, 164, 165
Population curves, 130
density maps, 221
370
GRAPHIC METHODS
Portland, Oregon, 208
Power development in United States, 239
Presidential election analysis, 10
Princeton graduates, class of 1901, 73
Princeton University, 111
Production schedule curves, 150
Profile drawings, 211
Progress photographs, 50, 51
Progressive averages, 153
Prominent bar for contrast, 30
Prout, Curtis, ii-
Proportions of charts, 355, 356
Prosperity charts, 104
Prussia, distribution of wealth in, 197
Pujo Money Report, 13
Punched-card tabulating machines, 320,
321, 322, 323, 324
Purchasing-department curves, 293
Queen Quality shoes, advertisement, 233
Races in population of the world, 4
Railway Age-Gazette, 115, 142, 224
Railroad annual reports, 309
earnings in United States, 115
operating costs, 142, 143
Rank charts, 32, 63, 65, 66
Rea, Samuel, 308
Record departments for cities, 299
room for corporations, 292
Records for the executive, 288
needless, 285
Rectangular co-ordinates, 132
Reduction of earnings, 329, 330
Reducing glass, use of, 241, 329
Reduction in size of drawings, 241
Reflecting lantern for curves, 303
Reflectoscope for curves, 304
Reports of corporations, 307
Returns, election, 341
Revenues of railroads of United States, 257
Review of Reviews, 46, 47, 229, 231
Rittenhouse, Elmer, 175, 351, 352
Road signs, Japanese, 346
Roads in New York State, map, 222
Routing charts, 17
Routing of papers in an office, 34
salesmen, 236
Royal Statistical Society, 205, 206
Rule, slide, 326, 328
Rules for graphic presentation, 361
Russell Sage Foundation, 24, 32, 33
St. Louis & San Francisco Railroad, 224
Sales analysis curves, 188, 269
Sales records by tabulating machines, 324
record map, 223
Salesmen, chart for ranking, 63
routing of, by pins, 226
San Francisco fire, 120, 121
"Satellite Cities", 214
Saturday Evening Post, 238
Savings-banks deposits in United States,
350
Scale arrangement for charts, 362
Scales, choice for horizontal and vertical,
352
double, for curves, 79
for charts, 8
on charts, rule for, 211
Scallop shells, 164
Schedule curves for factory output, 150
Schools of the United States, 32
Scientific American, the, 29
Scott, Roscoe, E., 337
Seaboard Air Line Railway, 177
Sections omitted from drawings, 190
Serial numbers for curves, 286
Shading, Ben Day, 331, 332
mechanical, 331, 332
Sheffield Scientific School, 111
Shipping of various countries, 24
Ships, length of, 49, 51
Shot-gun diagrams, 201
Significant figures, 326
Simple comparisons, 20
involving time, 36
Slide rule, use of, 326, 328
Slope of curves, 130, 131
Smoke deposits, measuring, 245
Smooth curves, 118, 119, 201, 357
Smoothing curves, 98
Solid models, 336
Soot deposits, measuring, 245
Sophie 19th, milk record, 278
Spot maps, 246
Standard corporation, 334
Standards for graphic presentations, 363
Statistical Atlas, 8, 28, 36, 65, 80, 130, 168,
172, 215
Statisticians for corporations, 293
Steam, cost of producing, 12
Steam turbine, tests of, 122
Steel, curves for strength of, 119
Steel plates, weight of, 333
Stockholders of corporations, number of, 308
Storage capacity curves, 159
Straw-board for mounting maps for pins,
230
for use with map pins, 191
INDEX
371
Street-car service map, 225
String for routing salesmen, 237
Stream velocity, 87
Swazey, Edward Scott, ii
Subdivision of components, 8
Suffern & Son, 30, 213
Survey, the, 6, 245
Swinging display fixtures for maps, 233
Symbols for charts, 345, 346
System, 15, 90, 123, 223.
Tabulating Machine Company, 322, 323,
324, 325
Tabulating machines, 320, 321, 322, 323,
324
machines for cards, 323
Tacks, celluloid-covered, for maps, 247,
248
map, 225, 247, 248
Tarr and McMurray's new geographies,
22
Taylor, Graham Romeyn, 214, 221
Telephone load curves, 108
rates, 126
service curves, 179
service in Wisconsin, 178
Telephones in United States, pin map,
240
number used in United States, 354
Temperature curves, 117, 118
Thompson, A. T. & Co., reflectoscope, 303
Thomson, H. F., 198
Three-dimensional charts, 205, 206
Time charts, 53
Time-distance charts, 64, 67
curves, 64, 67
Titles for charts, 344, 345
Topographical maps, 235
Totalizing curves, 125
Tracing cloth used with maps, 210
Trading centers in United States, 238
Train-dispatching charts, 61, 62, 67
Train-operation curves, 123
Transparentizing solution, 328
Trenton, N. J., public schools, 2
Trucks, costs for gasoline, 198
cost of operating, 29
Tuberculosis death rates, 351
Tug-boat operation, 58
Turbine, steam, tests of, 122
Two independent variables, charts for, 205,
206
Union Bag & Paper Co., 45
Union Pacific Railroad, 311, 312
United States Census Office methods, 320,
321
United States Steel Corporation, 313, 314
University of Cincinnati, 46, 47, 229, 231
Vacation chart, 53
Variables for curves, 84
Variables, two independent, 333
Velocity of water in streams, 87
Vertical arrangement of curves, 347, 349
bar charts, 354
bars, 46, 47
for components, 138
Wage charts, 180, 181, 182
comparison on railroads, 49
Wall board, 232
charts, 306
exhibits, 358
maps, 225, 229
Wall Street Journal, 308
Warne, Frank J., 103
W'ater power in United States, 216
Water storage-capacity curves, 159
Wave lengths on curves, 283
Waves in curves, 97
Wavy line for bottom of chart, 350, 352,
362
Weather cnarts, 93
Wealth, curves showing distribution, 197
WTeight of steel plates chart, 333
Weighted averages, 103
Westinghouse Electric & Manufacturing
Co., 295
Westinghouse, George, 31
Wheat, production of, 1910, 27
Wheeling & Lake Erie Railroad 1 02
Whipple, George C., 95
White, William Pierrepont, 222
Worcester Polytechnic Institute, 204
World's Work, the, 39, 40, 43, 49, 51, 211
Worsted mill operation, 52, 54
Yale University, 111, 212
Years, methods for naming on curves, 82
Yule, G. Udny, ii
Zero lines for curves, 82, 140, 350, 351, 352
Zero lines on curve cards, 271
Zizek, Franz, ii
Live Music
Archive
Librivox
Free Audio
Metropolitan Museum
Cleveland
Museum of Art
Internet
Arcade
Console Living Room
Open Library
American
Libraries
TV News
Understanding
9/11